Additional Questions - Chapter 11 Waves 11th Science Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated On May 15, 2024

By SaraNextGen

Additional Questions Solved
I. Choose the correct answer from the following:
Question 1.
Mechanical Waves
(a) are longitudinal only
(b) are transverse only
(c) can be both longitudinal and transverse.
(d) are neither longitudinal for transverse waves.
Answer:
(c) can be both longitudinal and transverse.
Question 2.
Sound whose frequency is $50 \mathrm{~Hz}$ ?
(a) has a relatively short wavelength.
(b) has a relatively long wavelength
(c) is very loud
(d) is very intense

Answer:
(a) has a relatively short wavelength.
Question 3.
Sound travels fastest in ......
(a) Steel
(b) air
(c) water
(d) vaccum
Answer:
(a) steel
Question 4.
A boat at anchor is rocked by waves of velocity $25 \mathrm{~m} / \mathrm{s}$, having crests $100 \mathrm{~m}$ apart. The boat bounches up once in every
(a) $4.0 \mathrm{~s}$
(b) $2500 \mathrm{~s}$
(c) $0.25 \mathrm{~s}$
(d) $75 \mathrm{~s}$
Answer:
(a) $4.0 \mathrm{~s}$
Hint:
$\lambda=$ distance between crests $=100 \mathrm{~m}$ frequency $\mathrm{v}=\frac{25}{100}=\frac{1}{4} \mathrm{~s}^{-1}$
Therefore, the crests reach the boat once every 4 seconds.
Question 5.
Choose the correct statement:
(a) sound waves are transverse waves
(b) sound travels fastest through vaccum.
(c) sound travels faster in solids than in gases.
(d) sound travels faster in gases than in liquids.
Answer:
(c) sound travels faster in solids than in gases.
Question 6.
Transverse waves can propagate ......
(a) both in a gas and in a metal
(b) in a gas but not in a metal
(c) not in a gas but in a metal
(d) neither in a gas nor in a metal

Answer:
(a) not in a gas but in a metal.
Question 7.
The speed of the wave represented by $\mathrm{y}=\mathrm{A} \sin (\omega \mathrm{t}-\mathrm{kx})$ is .......
(a) $\mathrm{k} / \omega$
(b) $\omega / \mathrm{k}$
(c) $\omega \mathrm{k}$
(d) $1 / \omega \mathrm{k}$
Answer:
(b) $\omega / \mathrm{k}$
Question 8.
The equation of a wave travelling in a string can be written as $y=3 \cos \{\pi(100 t-x)\}$ where $y$ and $x$ are in $\mathrm{cm}$ and $t$ is in seconds. Then the value of wavelength is ......
(a) $100 \mathrm{~cm}$
(b) $2 \mathrm{~cm}$
(c) $50 \mathrm{~cm}$
(d) $4 \mathrm{~cm}$
Answer:
(b) $2 \mathrm{~cm}$
Hint:
On comparing given equation with $\mathrm{y}=\mathrm{A} \cos (\mathrm{kx}-\omega \mathrm{t})$, we get
$
\lambda=\frac{2 \pi}{k}=\frac{2 \pi}{\pi}=2 \mathrm{~cm} \quad[\therefore k=\pi]
$
Question 9.
A wave of frequency $500 \mathrm{Hzhas}$ a velocity $300 \mathrm{~m} / \mathrm{s}$. The distance between two nearest points which are $60^{\circ}$ out of phase, is ......
(a) $0.2 \mathrm{~m}$

(b) $0.1 \mathrm{~m}$
(c) $0.4 \mathrm{~m}$
(d) $0.5 \mathrm{~m}$
Answer:
(a) $0.1 \mathrm{~cm}$
Hint: $\lambda=\frac{300}{500}=0.6 \mathrm{~m}$
$
\Delta x=\frac{\lambda}{2 \pi} \cdot \Delta \phi=\frac{0.6}{2 \pi} \cdot \frac{\pi}{3}=0.1 \mathrm{~m}
$
Question 10.
The equation of a wave travelling on a string is
$
y=4 \sin \left\{\frac{\pi}{2}\left(8 t-\frac{x}{8}\right)\right\}, \text { where } \mathrm{x}, \mathrm{y}
$
are in $\mathrm{cm}$ and $t$ in seconds. The velocity of the waves is
(a) $64 \mathrm{~cm} / \mathrm{s}$ in $-\mathrm{x}$ direction
(b) $32 \mathrm{~cm} / \mathrm{s}$ in $-x$ direction
(c) $32 \mathrm{~cm} / \mathrm{s}$ in $+\mathrm{x}$ direction
(d) $64 \mathrm{~cm} / \mathrm{s}$ in $+\mathrm{x}$ direction
Answer:
(d) $64 \mathrm{~cm} / \mathrm{s}$ in $+\mathrm{x}$ direction to $\mathrm{S}$
Hint: Velocity $v=\frac{\omega}{k}=\frac{8}{1 / 8}=64 \mathrm{~cm} / \mathrm{s}$ in $+x$ direction.

Question 11.
The equation of a wave is
$
y=4 \sin \left\{\frac{\pi}{2}\left(2 t+\frac{x}{8}\right)\right\}
$
where $\mathrm{y}, \mathrm{x}$ are in $\mathrm{cm}$ and $\mathrm{t}$ in seconds. The amplitude wavelength, velocity and frequency of the wave are, respectively, ......
(a) $4 \mathrm{~cm}, 32 \mathrm{~cm}, 16 \mathrm{~cm} / \mathrm{s}, 0.5 \mathrm{~Hz}$
(b) $8 \mathrm{~cm}, 16 \mathrm{~cm}, 32 \mathrm{~cm} / \mathrm{s}, 1.0 \mathrm{~Hz}$
(c) $4 \mathrm{~cm}, 32 \mathrm{~cm}, 32 \mathrm{~cm} / \mathrm{s}, 0.5 \mathrm{~Hz}$
(d) $8 \mathrm{~cm}, 16 \mathrm{~cm}, 16 \mathrm{~cm} / \mathrm{s}, 1.0 \mathrm{~Hz}$
Answer:
(a) $4 \mathrm{~cm}, 32 \mathrm{~cm}, 16 \mathrm{~cm} / \mathrm{s}, 0.5 \mathrm{~Hz}$
Question 12.
The diagram shows the profile of a wave, which of the following pairs of points are in phase?
(a) A, B
(b) $\mathrm{B}, \mathrm{C}$
(c) B, D
(d) B, E

Answer:
(d) B, E
Question 13.
Ultrasonic waves are those waves which
(a) human beings cannot hear
(b) human beings can hear
(c) have high velocity
(d) have large amplitude
Answer:
(a) human beings cannot hear
Question 14.
A transverse wave of amplitude $0.5 \mathrm{~m}$, wavelength $1 \mathrm{~m}$ and frequency $2 \mathrm{~Hz}$ is propogating in a string in the negative $\mathrm{x}$ direction. The equation of this wave is ....
(a) $y=0.5 \sin (2 \pi x-4 \pi t)$
(b) $y=0.5 \sin (2 \pi x+4 \pi t)$
(c) $y=0.5 \sin (\pi x-2 \pi \mathrm{t})$
(d) $y=0.5 \cos (\mathrm{kx}-2 \pi \mathrm{t})$
Answer:
(b) $y=0.5 \sin (2 \pi x+4 \pi t)$
Hint:
$\mathrm{y}=\mathrm{A} \sin (\mathrm{kx}+\omega \mathrm{t})$
Here $\mathrm{A}=0.5 \mathrm{~m}$
Hint: $\quad y=\mathrm{A} \sin (k x+\omega t)$
Here $\quad A=0.5 \mathrm{~m}$
$
\begin{aligned}
& k=\frac{2 \pi}{\lambda}=\frac{2 \pi}{1}=2 \pi \mathrm{m}^{-1} ; \omega=2 \pi f=4 \pi \mathrm{rad} / \mathrm{s} \\
& \Rightarrow \quad y=0.5 \sin (2 \pi x+4 \pi t) .
\end{aligned}
$
Question 15.
With the rise of temperature, the speed of sound in a gas ........
(a) increases
(b) decreases
(c) remain the same
(d) may increase or decrease depending on the corresponding change in pressure.
Answer:

(a) increases
Question 16.
Speed of sound in a gas in proportional to .......
(a) square root of isothermal elasticity
(b) square root of adiabatic elasticity
(c) isothermal elasticity
(d) adiabatic elasticity
Answer:
(b) square root of adiabatic elasticity
Question 17.
The velocity of sound in are is not affected by change in the
(a) atmospheric pressure
(b) moisture content of air
(c) temperature of air
(d) composition of air
Answer:
(a) atmospheric pressure
Question 18.
A longitudinal wave is described by the equation $y=y_0 \sin 2 \pi(f t-x / \lambda)$. The maximum particle velocity is equal to four times the wave velocity if $. . \ldots .$.
(a) $\lambda=\pi y_0 / 4$
(b) $\lambda=\pi y_0 / 2$
(c) $\lambda=4 \pi y_0$
(d) $\lambda=$
Answer:
Particle velocity $\quad v=\frac{d y}{d t}=2 \pi y_0 \cos \{2 \pi(f t-x / \lambda)\}$

$
\begin{aligned}
v_{\max } & =2 \pi f y_0 \\
v_{\max } & =2 \pi f y_0=4 f \lambda \\
\Rightarrow \quad \lambda & =\frac{\pi y_0}{2}
\end{aligned}
$
Question 19.
If $\mathrm{v}_0$ and $\mathrm{v}$ denote the sound velocity and the rms velocity of the molecules in a gas, then
(a) $v_0=v(3 \backslash \gamma)^{1 / 2}$
(b) $v_0=0$
(c) $v_0=v(\gamma \backslash 3)^{1 / 2}$
(d) $v_0$ and $v$ are not related
Answer:
(c) $v_0=v(\gamma \backslash 3)^{1 / 2}$
Hint: $\quad v_0=\sqrt{\frac{\gamma \mathrm{RT}}{\mathrm{M}}} ; v=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}} \Rightarrow \frac{v_o}{v}=\sqrt{\frac{\gamma}{3}} \Rightarrow v_0=v\left(\frac{\gamma}{2}\right)^{\frac{1}{2}}$
Question 20.
With the propagation of a longitudinal wave through a material medium, the quantities transferred in the direction of propagation are ........
(a) energy, momentum and mass
(b) energy and momentum
(c) energy and mass
(d) energy

Answer:
(b) energy and momentum
Question 21.
If the amplitude of sound is doubled and the frequency reduced to one-fourth, the intensity will
(a) increase by a factor of 2
(b) decrease by a factor of 2
(c) decrease by a factor of 4
(d) remain unchanged
Answer:
(c) decrease by a factor of 4
Hint: I $\propto \omega^2 \mathrm{~A}^2$
$
\Rightarrow \frac{I^{\prime}}{\mathrm{I}}=\left(\frac{\omega^{\prime}}{\omega}\right)^2\left(\frac{\mathrm{A}^{\prime}}{\mathrm{A}}\right)^2=\left(\frac{1}{4}\right)^2(2)^2=\frac{1}{4}
$
Question 22.
When a source of sound is in motion towards a stationary observer, the effect observed is
(a) increase in the velocity of sound only
(b) decrease in the velocity of sound only
(c) increase in frequency of sound only
(d) increase in both the velocity and the frequency of sound
Answer:
(c) increase in frequency of sound only

Question 23.
The apparent wavelength of the light from a star, moving away from the earth, is $0.01 \%$ more than its real wave length. The speed of the star with respect to the earth is ......
(a) $10 \mathrm{~km} / \mathrm{s}$
(b) $15 \mathrm{~km} / \mathrm{s}$
(c) $30 \mathrm{~km} / \mathrm{s}$
(d) $60 \mathrm{~km} / \mathrm{s}$
Answer:
(c) $30 \mathrm{~km} / \mathrm{s}$
Hint: $\frac{v_r}{c}=\frac{\Delta \lambda}{\lambda}$ or $v_r=\frac{0.01}{100} \times 3 \times 10^8=3 \times 10^4 \mathrm{~m} / \mathrm{s}=30 \mathrm{~km} / \mathrm{s}$
Question 24.
The frequency of a radar is $780 \mathrm{MHz}$. When it is reflected from an approaching aeroplane the opponent frequency is more than the actual frequency by $2.6 \mathrm{kHz}$. The speed of the aeroplane is ......
(a) $0.25 \mathrm{~km} / \mathrm{s}$
(b) $0.5 \mathrm{~km} / \mathrm{s}$
(c) $1.0 \mathrm{~km} / \mathrm{s}$
(d) $2.0 \mathrm{~km} / \mathrm{s}$
Answer:
(b) $0.5 \mathrm{~km} / \mathrm{s}$
Hint: $\begin{aligned} & v^{\prime}= \frac{c+f}{c-f} v \Rightarrow v^{\prime}-v=\left[\frac{c+f}{c-f}-1\right] v \quad[v=c] \\ & \Rightarrow \Delta v=\frac{2 v f}{c-f} \approx \frac{2 v f}{c} \Rightarrow v=\frac{2 \Delta v}{2 v}=\frac{3 \times 10^8 \times 2.6 \times 10^3}{2 \times 780 \times 10^6}=0.5 \times 10^3 \mathrm{~m} / \mathrm{s}\end{aligned}$
Question 25.
The temperature at which the speed of sound in air becomes double its value at $27^{\circ} \mathrm{C}$ is
(a) $54^{\circ} \mathrm{C}$
(b) $327^{\circ} \mathrm{C}$
(c) $927^{\circ} \mathrm{C}$
(d) $-123^{\circ} \mathrm{C}$
Answer:
(c) $927^{\circ} \mathrm{C}$

$
\text { Hint: } \frac{v_2}{v_1}=\sqrt{\frac{273+t_2}{273+t_1}} \Rightarrow(2)^2=\frac{273+t_2}{273+27} \Rightarrow t_2=927^{\circ} \mathrm{C}
$
Question 26.
The equation of a transverse wave is given by $\mathrm{y}=10 \sin \{\pi(0.01 \mathrm{x}-2 \mathrm{t})\}$ where $\mathrm{y}$ and $\mathrm{x}$ are in $\mathrm{cm}$ and $\mathrm{t}$ is in seconds. Its frequency is
(a) $10 \mathrm{~s}^{-1}$
(b) $2 \mathrm{~s}^{-1}$
(c) $1 \mathrm{~s}^{-1}$
(d) $0.01 \mathrm{~s}^{-1}$
Answer:
(c) $1 \mathrm{~s}^{-1}$
Hint:
Comparing with the standard equation $\mathrm{y}=\mathrm{A} \sin (\mathrm{kx}-\omega \mathrm{t})$,
We have
$
\omega=2 \pi
$
Therefore, Frequency $f=\frac{2 \pi}{\omega}=1 \mathrm{~s}^{-1}$
Question 27.
When sound waves travel from air to water, which of the following remains constant?
(a) velocity
(b) frequency
(c) wavelength
(d) all of these
Answer:
(b) frequency

Question 28.
The speed of sound in oxygen is $332 \mathrm{~m} / \mathrm{s}$ at STP. The speed of sound in hydrogen at STP will be ........
(a) $53 / 2 \mathrm{~m} / \mathrm{s}$
(b) $2546 \mathrm{~m} / \mathrm{s}$
(c) $1328 \mathrm{~m} / \mathrm{s}$
(d) $664 \mathrm{~m} / \mathrm{s}$
Answer:
(c) $1328 \mathrm{~m} / \mathrm{s}$
Hint: $v=\sqrt{\frac{\gamma \mathrm{RT}}{\mathrm{M}}}$
$\gamma$ is same for both the gases, so, $\frac{v_{H_2}}{v_{\mathrm{O}_2}}=\sqrt{\frac{\mathrm{M}_{\mathrm{O}_2}}{\mathrm{M}_{\mathrm{H}_2}}}=\sqrt{\frac{32}{2}}=4$
$
\Rightarrow \quad f_{\mathrm{H}_2}=4 \times 332=1328 \mathrm{~m} / \mathrm{s}
$
Question 29.
If $\mathrm{v}_{\mathrm{a}}, \mathrm{v}_{\mathrm{h}}$, and $\mathrm{v}_{\mathrm{m}}$ are the speeds of sound in air, hydrogen and a metal at the same temperature, then
(a) $v_h>v_{\mathrm{a}}>v_m$
(b) $v_m>v_h>v_a$
(c) $v_h>v_m>v_a$
(d) $\mathrm{v}_{\mathrm{a}}>\mathrm{v}_{\mathrm{h}}>\mathrm{v}_{\mathrm{m}}$
Answer:
(b) $\mathrm{v}_{\mathrm{m}}>\mathrm{v}_{\mathrm{h}}>\mathrm{v}_{\mathrm{a}}$

Question 30.
Ultrasonic waves can be detected by
(a) telephone
(b) Hebb's method
(c) Kundt's tube
(d) Quincke's tube
Answer:
(c) Kundt's tube
Question 31.
The velocity of sound in a gas depends on ....
(a) Wavelength only
(b) density and elasticity of gas
(c) intensity only
(d) amplitude and frequency
Answer:
(b) density and elasticity of gas
Question 32.
When sound waves travel from air to water, which of these remains constant?
(a) velocity
(b) wavelength
(c) frequency
(d) all the above
Answer:
(c) frequency
Question 33.
When a wave goes from one medium to another, there is a change in
(a) velocity
(b) amplitude
(c) wavelength

(d) all the above
Answer:
(d) all the above
Question 34.
The equation of a sound wave is $y=0.0015 \sin (62.8 x+316 t)$. Find the wave length of the above .....
(a) 0.2 units
(b) 0.3 units
(c) 0.1 units
(d) 0.15 units
Answer:
(c) 0.1 units
Hint: $k=62.8$ units ; $\lambda=\frac{2 \pi}{k}=\frac{2 \times 3.14}{62.8}=0.1$ units
Question 35 .
Red shift is an illustration of
(a) low temperature emission
(b) high frequency absorption
(c) Doppler effect
(d) Same unknown Phenomenon.
Answer:
(c) Doppler effect
Question 36.
The ratio of the velocity of sound in a monatomic gas to that in a triatomic gas having same molar mass, under similar conditions of temperature and pressure, is .........
(a) 1.12
(6) 1.25
(c) 1.50
(d) 1.6
Answer:
(a) 1.12
Hint: $v=\sqrt{\frac{\gamma \mathrm{RT}}{\mathrm{M}}} \Rightarrow \sqrt{\frac{\gamma_{\text {mono }}}{\gamma_{t r i}}}=\sqrt{\frac{(5 / 3)}{(4 / 3)}}=\sqrt{1.25}=1.12$

Question 37.
Doppler shift in frequency does not depend upon .......
(a) the actual frequency of the wave
(b) the velocity of the source from the listener.
(c) the velocity of the source.
(d) the velocity of the observer.
Answer:
(b) the velocity of the source from the listener.
Question 38 .
If the density of oxygen is 16 times that of hydrogen, what will be the ratio of the velocities of sound in them?
(a) $1: 4$
(b) $4: 1$
(c) $2: 1$
(d) $1: 16$
Answer:
(a) $1: 4$
Hint: Using eq. $\frac{v_1}{v_2}=\sqrt{\frac{\rho_2}{\rho_1}} \frac{v_{\mathrm{O}_2}}{v_{\mathrm{H}_2}}=\sqrt{\frac{\rho_{\mathrm{H}_2}}{\rho_{\mathrm{O}_2}}}=\sqrt{\frac{1}{16}}=\frac{1}{4}$
Question 39.
Pitch of sound depends on ......
(a) frequency
(b) wavelength
(c) amplitude
(d) speed
Answer:
(a) frequency

Question 40.
The path difference between the two waves $y_1=a_1 \sin \left(\omega t-\frac{2 \pi x}{\lambda}\right)$ and $y_2=a_2 \cos \left(\omega t-\frac{2 \pi x}{\lambda}+\phi\right)$ is
(a) $\frac{\lambda}{2 \pi} \phi$
(b) $\frac{\lambda}{2 \pi}\left(\phi+\frac{\pi}{2}\right)$
(c) $\frac{2 \pi}{\lambda}\left(\phi+\frac{\pi}{2}\right)$
Answer:
(b) $\frac{\lambda}{2 \pi}\left(\phi+\frac{\pi}{2}\right)$
Hint: Phase difference $=\phi+\frac{\pi}{2} ;$ Path difference $=\frac{\lambda}{2 \pi}\left(\phi+\frac{\pi}{2}\right)$
Question 41.
Which of the following equations represents a wave?
(a) $\mathrm{y}=\mathrm{A}(\omega \mathrm{t}-\mathrm{kx})$
(b) $y=A \sin \omega t$
(c) $y=A \cos \mathrm{kx}$
(d) $y=A \sin (a t-b x+c)$
Answer:

(d) $y=A \sin (a t-b x+c)$
Question 42.
A wave travels in a medium according to the equation of displacement given by $\mathrm{y}(\mathrm{x}, \mathrm{t})$ $=0.03 \sin \{\pi(2 \mathrm{t}-0.01 \mathrm{x})\}$ where $\mathrm{y}$ and $\mathrm{x}$ are in metres and $\mathrm{t}$ in seconds. The wave length of the wave is .....
(a) $200 \mathrm{~m}$
(b) $100 \mathrm{~m}$
(c) $20 \mathrm{~m}$
(d) $10 \mathrm{~m}$
Answer:
(a) $200 \mathrm{~m}$
Hint: $\lambda=\frac{2 \pi}{k}=\frac{2 \pi}{0.01 \pi}=200 \mathrm{~m}$
Question 43.
The equation of a wave moving on string is $\mathrm{y}=8 \sin \{\pi(0.002 \mathrm{x}-4 \mathrm{t})\}$ where $\mathrm{x}, \mathrm{y}$ are in centimeter and $t$ in seconds. The velocity of the wave is ......
(a) $100 \mathrm{~cm} / \mathrm{s}$
(b) $0.2 \pi \mathrm{cm} / \mathrm{s}$
(c) $4 \pi \mathrm{cm} / \mathrm{s}$
(d) $200 \mathrm{~cm} / \mathrm{s}$
Answer:
(d) $200 \mathrm{~cm} / \mathrm{s}$
Hint: $v=\frac{\omega}{k}=\frac{4}{0.02}=200 \mathrm{~cm} / \mathrm{s}$.

Question 44.
If the velocity of sound in air is $340 \mathrm{~ms}^{-1}$, a person singing a note of frequency $250 \mathrm{cps}$ is producing sound waves with a wavelength of
(a) 0.7
(b) $1.36 \mathrm{~cm}$
(c) $1.36 \mathrm{~m}$
(d) $85 \mathrm{~km}$
Answer:
(c) 1.36
Hint: $f^{\prime}=\frac{340}{250}=1.36 \mathrm{~m}$
Question 45.
Asa transverse wave strikes against a fixed end .......
(a) its phase changes by $180^{\circ}$, but velocity does not change.
(b) its phase does not change, but velocity changes
(c) its velocity changes and phase too changes by $180^{\circ}$
(d) nothing can be predicted about changes in its velocity and phase.
Answer:
(a) its phase changes by $180^{\circ}$, but velocity does not change
Question 46.
A source of sounds is travelling with a velocity of $40 \mathrm{~km} / \mathrm{hr}$ towards an observer and emits sound of frequency $2000 \mathrm{~Hz}$. If the velocity of sound is $1220 \mathrm{~km} / \mathrm{hr}$, then what is the apparent frequency heard by the observer?
(a) $2068 \mathrm{~Hz}$
(b) $2180 \mathrm{~Hz}$
(c) $2000 \mathrm{~Hz}$
(d) $1980 \mathrm{~Hz}$
Answer:
(a) $2068 \mathrm{~Hz}$
Hint: $f^{\prime}=\left(\frac{v}{v-v_s}\right) \times f=\frac{1220}{1220-40} \times 2000=2068 \mathrm{~Hz}$
Question 47.
A vehicle with a horn of frequency $n$ is moving with a velocity of $30 \mathrm{~m} / \mathrm{s}$ in a direction perpendicular to the straight line joining the observer and the vehicle. The observer perceives the sound to have a frequency $n+n_1$. Then (if the sound velocity in air is 300 $\mathrm{m} / \mathrm{s}$ )
(a) $\mathrm{n}_1=10 \mathrm{n}$
(b) $\mathrm{n}_1=0$
(c) $\mathrm{n}_1=-0.1 \mathrm{n}$
(d) $\mathrm{n}_1=0.1 \mathrm{n}$
Answer:
(b) $\mathrm{n}_1=0$
Hint:
No Doppler effect is observed if the source moves perpendicular to the line joining the source and the observer. Therefore, the correct choice is (b).
Question 48.
The Doppler effect is applicable for
(a) light waves
(b) sound waves
(c) space waves
(d) both (a) and (b)
Answer:
(d) both (a) and (b)
Question 49.
The speed of a wave in a medium is $760 \mathrm{~m} / \mathrm{s}$. If 3600 waves are passing through a point in the medium in 2 minutes, then its wavelength is ......
(a) $13.8 \mathrm{~m}$
(b) $25.3 \mathrm{~m}$
(c) $41.5 \mathrm{~m}$
(d) $57.2 \mathrm{~m}$
Answer:
(b) $25.3 \mathrm{~m}$

Hint: Frequency $n=\frac{3600}{120}=30 \mathrm{~Hz}$; Wavelength $\lambda=\frac{v}{n}=\frac{760}{30}=25.3 \mathrm{~m}$
Question 50.
If a sound wave travels from air to water, the quantity that remain unchanged is
(a) velocity
(b) wavelength
(c) frequency
(d) amplitude
Answer:
(c) frequency
Question 51.
Asa spherical wave propagates, ......
(a) the wave intensity remains constant
(b) the wave intensity decrease as the inverse of the distance from the source
(c) the wave intensity decreases as the inverse square of the distance from the source.
(d) The wave intensity decreases as the inverse cube of the distance from the source.
Answer:
(c) The wave intensity decreases as the inverse square of the distance from the source.
Question 52.
A source of sound and a listener are approaching each other with a speed of $40 \mathrm{~ms}^{-1}$. The apparent frequency of a note produced by the source is $400 \mathrm{~Hz}$. Then its true frequency is (velocity of sound in air $=360 \mathrm{~ms}^{-1}$ )
(a) $320 \mathrm{~Hz}$
(b) $400 \mathrm{~Hz}$
(c) $360 \mathrm{~Hz}$

(d) $420 \mathrm{~Hz}$
Answer:
(a) $320 \mathrm{~Hz}$
Hint: $f^{\prime}=\left(\frac{v+v_0}{v-v_s}\right) f \Rightarrow 400=\left[\frac{360+40}{360-40}\right] f \Rightarrow f=320 \mathrm{~Hz}$
Question 53.
Sound waves of wavelength greater than that of audible sound are called
(a) infrasonic waves
(b) ultrasonic waves
(c) sonic waves
(d) seismic waves
Answer:
(a) infrasonic waves
Question 54.
The frequency of a sound wave is/and its velocity is $\mathrm{v}$. If the frequency is increased to 4 $f$ the velocity of the wave will be:
(a) $\mathrm{v}$
(b) $2 \mathrm{v}$
(c) $4 \mathrm{v}$
(d) $\mathrm{v} / 4$
Answer:
(a) $\mathrm{v}$
Hint:
The velocity is a characteristic of the medium and, therefore, it remains constant.

Question 55.
Which of the following statement is untrue? The velocity of sound in a gas .......
(a) is independent of pressure
(b) increases with increase in temperature
(c) is dependent on molecular weight
(d) is greater in dry air than in moist air

Answer:
(d) is greater in dry air than in moist air
Question 56.
When a stone is dropped on the surface of still water, the waves produced are
(a) transverse
(b) longitudinal
(c) Stationary
(d) partly longitudinal and partly transverse.
Answer:
(d) Partly longitudinal and partly transverse.
Question 57.
The equation of a wave is $\mathrm{y}=0.1 \sin (100 \pi \mathrm{t}-\mathrm{kx})$ where $\mathrm{x}, \mathrm{y}$ are in metres and $\mathrm{t}$ in seconds. If - the velocity of the wave is $100 \mathrm{~m} / \mathrm{s}$, then the value of $\mathrm{k}$ is
(a) $1 \mathrm{~m}^{-1}$
(b) $2 m^{-1}$
(c) $\pi \mathrm{m}^{-1}$
(d) $2 \pi \mathrm{m}^{-1}$
Answer:
(c) $\pi \mathrm{m}^{-1}$
Question 58.
A transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} \mathrm{~kg} \mathrm{~m}^{-1}$ is represented by the equation, $\mathrm{y}=0.2 \sin (1.5 \mathrm{x}+60 \mathrm{t})$
Where $\mathrm{x}$ is in metres and $\mathrm{t}$ is in seconds. The tension in the string (in newtons) is:
(a) 0.24
(b) 0.48
(c) 1.20
(d) 1.80
Answer:
(a) 0.48

Hint: $v=\sqrt{\frac{\mathrm{T}}{m}}=\frac{\omega}{k} \Rightarrow \mathrm{T}=\left(\frac{\omega}{k}\right)^2 m=\left(\frac{60}{1.5}\right)^2 \times 3 \times 10^{-4}=0.48 \mathrm{~N}$
Question 59.
A transverse wave propagating along $\mathrm{x}$-axis is represented by
$
y(x, t)=8.0 \sin \left(0.5 \pi x-4 \pi t-\frac{\pi}{4}\right)
$
where $\mathrm{x}$ is in metres and $\mathrm{t}$ is in seconds. The speed of the wave is
(a) $0.5 \pi \mathrm{m} / \mathrm{s}$
(b) $\frac{\pi}{4} \mathrm{~m} / \mathrm{s}$
(c) $8 \mathrm{~m} / \mathrm{s}$
(d) $4 \pi \mathrm{rr}$
Answer:
(c) $8 \mathrm{~m} / \mathrm{s}$
Hint:
Hint: Comparing with the standard equation $y=\mathrm{A} \sin (k x-\omega t+\phi)$
We have
$
\begin{aligned}
\omega & =4 \pi, k=0.5 \pi \\
\nu & =\frac{\omega}{k}=\frac{4 \pi}{0.5 \pi}=8 \mathrm{~m} / \mathrm{s}
\end{aligned}
$
Question 60.
Two waves represented by the following equation are travelling in the same medium: $y_1$ $=5 \sin 2 \pi(75 \mathrm{t}-0.25 \mathrm{x})$ and $\mathrm{y}_2=10 \sin 2 \pi(150-0.25 \mathrm{x})$ The intensity ratio of the two waves is
(a) $1: 2$
(b) $1: 4$
(c) $1: 8$
(d) $1: 16$

Answer:
(b) $1: 4$
Hint: $I \propto A^2 \Rightarrow \frac{I_1}{I_2}=\left(\frac{A_1}{A_2}\right)^2=\left(\frac{5}{10}\right)^2=\frac{1}{4}$
Question 61.
A point source emits sound equally in all direction is a non-absorbing medium. Two points $P$ and $\mathrm{Q}$ are at distances of $2 \mathrm{~m}$ and $3 \mathrm{~m}$, respectively, from the source. The ratio of the intensities of the waves at $\mathrm{P}$ and $\mathrm{Q}$ is ......
(a) $3: 2$
(b) $4: 9$
(c) $2: 3$
(d) $9: 4$
Answer:
(d) $9: 4$
Hint: $\mathrm{I} \alpha \frac{1}{r^2} \Rightarrow \frac{\mathrm{I}_{\mathrm{P}}}{\mathrm{I}_{\mathrm{Q}}}=\left(\frac{r_{\mathrm{Q}}}{r_{\mathrm{P}}}\right)^2=\left(\frac{3}{2}\right)^2=\frac{9}{4}$
Question 62.
The waves produced by a motor boat sailing in water are
(a) transverse
(b) longitudinal
(c) longitudinal and transverse
(d) stationary
Answer:
(c) longitudinal and transverse

Question 63.
Doppler effect in sound is due to .........
(a) motion of source
(b) motion of observer
(c) relative motion of source and observer
(d) none of the above
Answer:
(c) relative motion of source and observer
Question 64.
The velocity of sound in air at NTP is $330 \mathrm{~m} / \mathrm{s}$. What will be its value when temperature is doubled and pressure is halved?
(a) $165 \mathrm{~m} / \mathrm{s}$
(b) $330 \mathrm{~m} / \mathrm{s}$
(c) $330 / \sqrt{2}$
(d) $300 / \sqrt{2} \mathrm{~m} / \mathrm{s}$
Answer:
(c) $330 / \sqrt{2}$
Hint:
There is no effect of change of pressure on the velocity of sound in air. Further, $v \propto$ $\sqrt{\mathrm{T}}$
Question 65.
Sound waves travel at $350 \mathrm{~m} / \mathrm{s}$ through warm air and at $3500 \mathrm{~m} / \mathrm{s}$ through brass. The wavelength of a $700 \mathrm{~Hz}$ acoustic wave as it enters brass from warm air
(a) increases by a factor 20
(b) increases by a factor 10
(c) decreases by a factor 20
(d) decreases by a factor 10
Answer:

(b) increase by a factor 10
Hint:
Since the frequency remains the same, we have
$
\frac{\lambda_{\text {brass }}}{\lambda_{\text {air }}}=\frac{v_{\text {brass }}}{v_{\text {air }}} \Rightarrow \lambda_{\text {brass }}=\frac{3500}{350} \lambda_{\text {air }}=10 \lambda_{\text {air }}
$
Question 66.
A train moving at a speed of $220 \mathrm{~m} / \mathrm{s}$ towards a stationary object, emits a sound of frequency $1000 \mathrm{~Hz}$. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the driver of the train is
(a) $3000 \mathrm{~Hz}$
(b) $3500 \mathrm{~Hz}$
(c) $4000 \mathrm{~Hz}$
(d) $5000 \mathrm{~Hz}$
Answer:
(d) $5000 \mathrm{~Hz}$
Hint: $f^{\prime}=\left(\frac{330+220}{330+220}\right) \times 1000=5000 \mathrm{~Hz}$
Question 67.
A source of sounds emitting waves of frequency $100 \mathrm{~Hz}$ and an observer $\mathrm{O}$ are located at same distance from each other The source is moving with a speed of $19.4 \mathrm{~ms}^{-1}$ at an angle of $60^{\circ}$ with the source-observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air $330 \mathrm{~ms}^{-}$ ${ }^1$ ) is

(a) $97 \mathrm{~Hz}$
(b) $100 \mathrm{~Hz}$
(c) $103 \mathrm{~Hz}$
(d) $106 \mathrm{~Hz}$
Answer:
(c) $103 \mathrm{~Hz}$
Hint: $f^{\prime}=\frac{v}{v-v_s \cos \theta}=\frac{330}{330-19.4 \cos 60^{\circ}} \times 100=103 \mathrm{~Hz}$
Question 68.
Beats occur because of
(a) interference
(b) reflection
(c) refraction
(d) Doppler effect
Answer:
(a) interference
Question 69.
A vibrating stretched string resonates with a tuning fork of frequency $512 \mathrm{~Hz}$ when the length of the string is $0.5 \mathrm{~m}$. The length of the string required to vibrate resonantly with a tuning fork of frequency $256 \mathrm{~Hz}$ would be .....
(a) $0.25 \mathrm{~m}$
(b) $0.75 \mathrm{~m}$
(c) $1.0 \mathrm{~m}$
(d) $2.0 \mathrm{~m}$
Answer:
(c) $1.0 \mathrm{~m}$

Hint: $v \propto \frac{1}{\mathrm{~L}} \Rightarrow \frac{\mathrm{L}_2}{\mathrm{~L}_1}=\frac{v_1}{v_2}$ or $\mathrm{L}_2=\frac{v_1}{v_2} \mathrm{~L}_1=\frac{512 \times 0.5}{256}=1.0 \mathrm{~m}$
Question 70.
A cylindrical tube, open at both ends has a fundamental frequency $f$ in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now .......
(a) $f / 2$
(b) $\mathrm{f}$
(c) $3 \mathrm{f} / 4$
(d) $2 \mathrm{f}$
Answer:
(a) $\mathrm{f}$
Hint:
When the tube is dipped in water, it become a closed pipe of length $\mathrm{L} / 2$. Its fundamental
frequency is
$
f^{\prime}=\frac{v}{4(\mathrm{~L} / 2)}=f
$
Question 71.
With the increase in temperature, the frequency of the found from an organ pipe
(a) decrease
(b) increase
(c) remains unchanged
(d) changes erractically

Answer:
(b) increase
Hint:
Frequency $\propto \mathrm{v} / \mathrm{L}$. Now $\mathrm{v}$ and $\mathrm{L}$ both increase with temperature but increase of $\mathrm{v}$ is much more than the increase of $\mathrm{L}$ which is negligible. Thus frequency increases with temperature.
Question 72.
Two waves of the same frequency and amplitude super impose to produce a resultant disturbance of the same amplitude. The phase difference between the waves is
(a) zero
(b) $\pi / 3$
(c) $\pi / 4$
(d) $2 \pi / 3$
Answer:
(d) $2 \pi / 3$
Hint:
Let the amplitude of each wave be A and phase difference between them be $\varphi$. Then,
$
A=\sqrt{A^2+A^2+2 A^2 \cos \phi} \Rightarrow \cos \phi=-\frac{1}{2} \text { or } \phi=\frac{2 \pi}{3}
$
Question 73.
A sonometer wire is vibrating in the second overtone. In the wire there are
(a) two nodes and two antinodes
(b) one node and two antinodes
(c) four nodes and three antinodes
(d) three nodes and three antinodes
Answer:
(c) four nodes and three antinodes

Question 74.
If a resonance tube is sounded with a tuning fork of frequency $256 \mathrm{~Hz}$, resonance occurs at $35 \mathrm{~cm}$ and $105 \mathrm{~cm}$. The velocity of sound is about ......
(a) $358 \mathrm{~m} / \mathrm{s}$
(b) $512 \mathrm{~m} / \mathrm{s}$
(c) $524 \mathrm{~m} / \mathrm{s}$
(d) none of these
Answer:
(a) $358 \mathrm{~m} / \mathrm{s}$
Hint:
$
v=2 f\left(\mathrm{~L}_2-\mathrm{L}_1\right)=2 \times 256 \times(105-35) \times 10^{-2}=358.4 \mathrm{~m} / \mathrm{s}
$
Question 75.
A wave of frequency $100 \mathrm{~Hz}$ is sent along a string towards a fixed end when this wave travels back after reflection, a node is formed at a distance of $10 \mathrm{~cm}$ from the fixed end of the string. The speed of the incident wave is ......
(a) $40 \mathrm{~m} / \mathrm{s}$
(b) $20 \mathrm{~m} / \mathrm{s}$
(c) $10 \mathrm{~m} / \mathrm{s}$
(d) $5 \mathrm{~m} / \mathrm{s}$
Answer:
(b) $20 \mathrm{~m} / \mathrm{s}$
Hint:
The fixed end is also a node distance between two nodes $=\frac{\lambda}{2}=10 \mathrm{~cm}$ or $\lambda=20 \mathrm{~cm}=0.2 \mathrm{~cm}$
Speed $\mathrm{v}=\mathrm{f} \lambda=100 \times 0.2=20 \mathrm{~m} / \mathrm{s}$
Question 76.
A standing wave is represented by $\mathrm{y}=\mathrm{A} \sin (100 \mathrm{t}) \cos (0.01 \mathrm{x})$ where $\mathrm{y}$ and $\mathrm{A}$ are in millimetres, $t$ in seconds and $\mathrm{x}$ in metres. The velocity of the wave is ........
(a) $10^4 \mathrm{~m} / \mathrm{s}$
(b) $1 \mathrm{~m} / \mathrm{s}$
(c) $10^{-4} \mathrm{~m} / \mathrm{s}$
(d) not derivable from the above information
Answer:
(a) $10^4 \mathrm{~m} / \mathrm{s}$
Hint: $v=\frac{\omega}{k}=\frac{100}{0.10}=10^4 \mathrm{~m} / \mathrm{s}$

Question 77.
Two waves of the same frequency and intensity superimpose with each other in opposite phases. Then after superposition the
(a) intensity increases to four times
(b) intensity increase to two times
(c) frequency increases to four times
(d) none of the above
Answer:
(d) none of the above
Hint:
Since the waves are in opposite phases, the resultant intensity will be zero. The frequency remains the same. So, the correct choice is (d).
Question 78.
Two open organ pipes of lengths $50 \mathrm{~cm}$ and $50.5 \mathrm{~cm}$ produce 3 beats $/ \mathrm{s}$. Then the velocity of sound is .......
(a) $300 \mathrm{~m} / \mathrm{s}$
(b) $30 \mathrm{~m} / \mathrm{s}$
(c) $303 \mathrm{~m} / \mathrm{s}$
(d) $30.3 \mathrm{~m} / \mathrm{s}$
Answer:
(c) $303 \mathrm{~m} / \mathrm{s}$
Hint: $\frac{v}{2 \times 50}-\frac{v}{2 \times 50.5}=3$ (or) $(101-100) v=100 \times 101 \times 3$ (or) $v=30300$
Question 79.
If the ratio of the amplitudes of two waves is $4: 3$, then the ratio of maximum and minimum intensities is ......
(a) $16: 9$
(b) $49: 16$
(c) $7: 1$
(d) $49: 1$
Answer:
(d) $49: 1$
Question 80.
An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency $256 \mathrm{~Hz}$, if the length of the column in centimeter is (velocity of sound in air $=340 \mathrm{~m} / \mathrm{s}$ )

(a) 21.25
(b) 125
(c) 62.50
(d) 33.2
Answer:
(d) 33.2
Hint:
$
f=\frac{v}{4 \mathrm{~L}} \Rightarrow \mathrm{L}=\frac{v}{4 f}=\frac{34000}{4 \times 256}=33.2 \mathrm{~cm}
$
Question 81.
Two sound waves with wavelengths $5.0 \mathrm{~cm}$ and $5.5 \mathrm{~cm}$, respectively each propagate in a gas with velocity $330 \mathrm{~m} / \mathrm{s}$. The number of beats per second will be .......
(a) 0
(b) 1
(c) 6
(d) 12
Answer:
(c) 6
Hint:
Number of beats $/ \mathrm{s}$ is $=330\left[\frac{1}{5}-\frac{1}{5.5}\right]=6$
Question 82.
Two vibrating tuning forks produce progressive waves given be $\mathrm{y}_1=4 \sin 500 \pi \mathrm{t}$ and $\mathrm{y}_2$ $=2 \sin 506 \pi \mathrm{t}$ where $\mathrm{t}$ is in seconds number of beats produced per minute is ........
(a) 60
(b) 3

(c) 369
(d) 180
Answer:
(d) 180
Hint: $v_1=\frac{500 \pi}{2 \pi}=250 \mathrm{~Hz} ; v_2=\frac{506 \pi}{2 \pi}=253 \mathrm{~Hz}$
Question 83.
The ratio of intensities of two waves is $16: 9$. If they produce interference, then the ratio of maximum and minium intensities will be
(a) $4: 3$
(b) $49: 1$
(c) $64: 27$
(d) $81: 49$
Answer:
(b) $49: 1$
$
\begin{aligned}
\text { Hint: Amplitude ratio } r=\sqrt{\frac{I_1}{I_2}}=\sqrt{\frac{16}{9}}=\frac{4}{3} \\
\frac{I_{\max }}{I_{\max }}=\left(\frac{r+1}{r-1}\right)^2=\left(\frac{4+3}{4-3}\right)^2=\frac{49}{1}
\end{aligned}
$

Question 84.
A closes organ pipe of length $20 \mathrm{~cm}$ is sounded with a tuning fork in resonance. What is the frequency of the tuning fork? $(\mathrm{v}=332 \mathrm{~m} / \mathrm{s})$
(a) $300 \mathrm{~Hz}$
(b) $350 \mathrm{~Hz}$
(c) $375 \mathrm{~Hz}$
(d) $415 \mathrm{~Hz}$
Answer:
(d) $415 \mathrm{~Hz}$ So,
Hint: In resonance, the frequency of the fork is equal to the frequency of the organ pipe, $f=\frac{v}{4 \mathrm{~L}}=\frac{332}{4 \times 0.2}=415 \mathrm{~Hz}$
Question 85.
In a resonance tube, the first resonance is obtained at $40 \mathrm{~cm}$ length, using a tuning fork of frequency $450 \mathrm{~Hz}$. Ignoring end correction, the velocity of sound in air is
(a) $620 \mathrm{~m} / \mathrm{s}$
(b) $720 \mathrm{~m} / \mathrm{s}$
(c) $820 \mathrm{~m} / \mathrm{s}$
(d) $1020 \mathrm{~m} / \mathrm{s}$
Answer:
(b) $720 \mathrm{~m} / \mathrm{s}$
Hint: $\frac{\lambda}{4}=40 \mathrm{~cm}=0.4 \mathrm{~m} \Rightarrow \quad \therefore \lambda=4 \times 0.4=1.6 \mathrm{~m} ; f=450 \mathrm{~Hz}$
Velocity of sound $\quad v=f \lambda=450 \times 1.6=720 \mathrm{~m} / \mathrm{s}$
Question 86.
If we study the vibration of a pipe open at both ends, then which of the following statement is not true?
(a) open end will be antinode
(b) odd harmonics of the fundamental frequency will be generated

(c) all harmonics of the fundamental
(d) pressure change will be maximum at both ends.
Answer:
(d) pressure change will be maximum at both ends.
Hint:
Pressure change at open ends is zero.
Question 87.
The fundamental frequency of a closes organ pipe of length $20 \mathrm{~cm}$ is equal to the second overtone of an organ pipe open at both the ends. The length of the organ pipe open at both the ends is ......
(a) $80 \mathrm{~cm}$
(b) $100 \mathrm{~cm}$
(c) $120 \mathrm{~cm}$
(d) $140 \mathrm{~cm}$
Answer:
(c) $120 \mathrm{~cm}$
Hint: $\frac{v}{4 \mathrm{~L}_{\text {closed }}}=\frac{3 v}{2 \mathrm{~L}_{\text {open }}} \Rightarrow \mathrm{L}_{\text {open }}=6 \mathrm{~L}_{\text {closed }}=120 \mathrm{~cm}$
2 Mark Questions
Question 1.
Define the term wave motion?
Answer:
Wave motion is a kind of disturbances which travels through a medium due to repeated vibrations of the particles of the medium about their mean positions, the disturbance being handed over from one particle to the next.
Question 2.
What is a progressive wave?
Answer:
A wave that travels from one point of the medium to another is called a progressive wave.
Question 3.
What is a plane progressive harmonic wave?
Answer:
If during the propagation of a wave through a medium the particles of the medium vibrate simple harmonically about their mean positions, than the wave is said to be plane progressive harmonic wave.
Question 4.
What do you mean by phase of a wave?
Answer:
The phase of a harmonic is a quantity that gives complete information of the wave at any time and at any position.
Question 5.
Define wave velocity or phase velocity?
Answer:
The distance covered by a wave in the direction of its propagation per unit time is called the wave velocity.
Question 6.
What are stationary waves?
Answer:
When two identical waves of same amplitude and frequency travelling in opposite directionals with the same speed along the same path superpose each other, the resultant wave does not travel in the either direction and is called stationary or standing waves.
Question 7.
What is meant by threshold of heating?
Answer:
The lowest intensity of sound that can be perceived by the human ear is called threshold of hearing. For a sound of frequency $10 \mathrm{kHz}$, the threshold of hearing is $10^{-12} \mathrm{Wm}^{-2}$
Question 8.
What is meant by reverberation?

Answer:
The persistence of audible sound after the source has ceased to emit sound is called reverberation.
Question 9.
What is musical scale?
Answer:
A series of notes whose fundamental frequencies have definite ratios and which produce a pleasing effect on the ear when sounded in succession constitute a musical scale.
Question 10.
Define reverberation time?
Answer:
It is defined as the time which sound takes to fall in intensity to one millionth $\left(10^{-6}\right)$ part of its original intensity after it was stopped.