Waves - NCERT based PYQs

1.

The two nearest harmonics of a tube closed at one end and open at the other end are $220$ Hz and $260$ Hz. What is the fundamental frequency of the system?

1.	$20$ Hz	2.	$30$ Hz
3.	$40$ Hz	4.	$10$ Hz

2.

Two cars moving in opposite directions approach each other at speeds of 22 m/s and 16.5 m/s, respectively. The driver of the first car blows a horn with a frequency of 400 Hz. The frequency heard by the driver of the second car is [assume velocity of sound to be 340 m/s]:
1. 361 Hz
2. 411 Hz
3. 448 Hz
4. 350 Hz

3. The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe $L$ meter long. The length of the open pipe will be:

1.	$L$	2.	$2L$
3.	$\dfrac{L}{2}$	4.	$4L$

4.

Three sound waves of equal amplitudes have frequencies of $(n-1),~n,$ and $(n+1).$ They superimpose to give beats. The number of beats produced per second will be:

1.	$1$	2.	$4$
3.	$3$	4.	$2$

5. A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of $27^{\circ}\text{C}$, to successive resonances are produced at $20$ cm and $73$ cm column length. If the frequency of the tuning fork is $320$ Hz, the velocity of sound in air at $27^{\circ}\text{C}$ is:

1.	$330$ m/s	2.	$339$ m/s
3.	$350$ m/s	4.	$300$ m/s

6. The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is $20~\text{cm}$, the length of the open organ pipe is:

1.	$13.2~\text{cm}$	2.	$8~\text{cm}$
3.	$12.5~\text{cm}$	4.	$16~\text{cm}$

7.

A siren emitting a sound of frequency $800$ Hz moves away from an observer towards a cliff at a speed of $15$ ms^-1. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is:
(Take, the velocity of sound in air = $330$ ms^-1)
1. $800$ Hz
2. $838$ Hz
3. $885$ Hz
4. $765$ Hz

8. An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is $50~\text{cm}.$ The next larger length of the column resonating with the same tuning fork will be:

1.	$100~\text{cm}$	2.	$150~\text{cm}$
3.	$200~\text{cm}$	4.	$66.7~\text{cm}$

9.

A uniform rope, of length $L$ and mass $m_1,$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda_2.$ The ratio $\frac{\lambda_2}{\lambda_1}$ is:

1.	$\sqrt{\dfrac{m_1+m_2}{m_2}}$	2.	$\sqrt{\dfrac{m_2}{m_1}}$
3.	$\sqrt{\dfrac{m_1+m_2}{m_1}}$	4.	$\sqrt{\dfrac{m_1}{m_2}}$

10.

A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 ms^-1 at an angle of $60^{0}$ 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 ms^-1), is:

1. 100 Hz
2. 103 Hz
3. 106 Hz
4. 97 Hz

11.

$4.0~\text{gm}$ of gas occupies $22.4~\text{litres}$ at NTP. The specific heat capacity of the gas at a constant volume is $5.0~\text{JK}^{-1}\text{mol}^{-1}.$ If the speed of sound in the gas at NTP is $952~\text{ms}^{-1},$ then the molar heat capacity at constant pressure will be:
($R=8.31~\text{JK}^{-1}\text{mol}^{-1}$)

1.	$8.0~\text{JK}^{-1}\text{mol}^{-1}$	2.	$7.5~\text{JK}^{-1}\text{mol}^{-1}$
3.	$7.0~\text{JK}^{-1}\text{mol}^{-1}$	4.	$8.5~\text{JK}^{-1}\text{mol}^{-1}$

12. A string is stretched between fixed points separated by $75.0~\text{cm}$. It is observed to have resonant frequencies of $420~\text{Hz}$ and $315~\text{Hz}$. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is:

1.	$ 155~\text{Hz} $	2.	$ 205~\text{Hz} $
3.	$ 10.5~\text{Hz} $	4.	$ 105~\text{Hz} $

13.

The fundamental frequency of a closed organ pipe of a length $20$ cm is equal to the second overtone of an organ pipe open at both ends. The length of the organ pipe open at both ends will be:

1.	$80$ cm	2.	$100$ cm
3.	$120$ cm	4.	$140$ cm

14.

If $n_1$, $n_2$_, and $n_3$are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by:

1.	$ \frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$
2.	$ \frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n_1}}+\frac{1}{\sqrt{n_2}}+\frac{1}{\sqrt{n_3}}$
3.	$ \sqrt{n}=\sqrt{n_1}+\sqrt{n_2}+\sqrt{n_3}$
4.	$ n=n_1+n_2+n_3$

15.

The number of possible natural oscillations of the air column in a pipe closed at one end of length $85$ cm whose frequencies lie below $1250$ Hz are:
(velocity of sound= $340~\text{m/s}$)

1.	$4$	2.	$5$
3.	$7$	4.	$6$

16.

A speeding motorcyclist sees a traffic jam ahead of him. He slows down to 36 km/hour. He finds that traffic has eased and a car moving ahead of him at 18 km/hour is honking at a frequency of 1392 Hz. If the speed of sound is 343 m/s, the frequency of the honk as heard by him will be:
1. 1332 Hz
2. 1372 Hz
3. 1412 Hz
4. 1454 Hz

17. If we study the vibration of a pipe open at both ends, then which of the following statements is not true:

1.	Odd harmonics of the fundamental frequency will be generated.
2.	All harmonics of the fundamental frequency will be generated.
3.	Pressure change will be maximum at both ends.
4.	The open end will be an antinode.

18.

A source of unknown frequency gives $4$ beats/s when sounded with a source of known frequency of $250~\text{Hz}.$ The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency of $513~\text{Hz}.$ The unknown frequency will be:

1.	$246~\text{Hz}$	2.	$240~\text{Hz}$
3.	$260~\text{Hz}$	4.	$254~\text{Hz}$

19.

A wave traveling in the +ve $x\text-$direction having maximum displacement along $y\text-$direction as $1~\text{m}$, wavelength $2\pi~\text{m}$ and frequency of $\frac{1}{\pi}~\text{Hz}$, is represented by:

1.	$y=\sin (2 \pi x-2 \pi t)$	2.	$y=\sin (10 \pi x-20 \pi t)$
3.	$y=\sin (2 \pi x+2 \pi t)$	4.	$ y=\sin (x-2 t)$

20.

When a string is divided into three segments of lengths $l_1$, $l_2$ and $l_3$, the fundamental frequencies of these three segments are $\nu_1$, $\nu_2$ and $\nu_3$ respectively. The original fundamental frequency ($\nu$) of the string is:

1.	$\sqrt{\nu} = \sqrt{\nu_1}+\sqrt{\nu_2}+\sqrt{\nu_3}$
2.	$\nu = \nu_1+\nu_2+\nu_3$
3.	$\dfrac{1}{\nu} =\dfrac{1}{\nu_1} +\dfrac{1}{\nu_2}+\dfrac{1}{\nu_3}$
4.	$\dfrac{1}{\sqrt{\nu}} =\dfrac{1}{\sqrt{\nu_1}} +\dfrac{1}{\sqrt{\nu_2}}+\dfrac{1}{\sqrt{\nu_3}}$

21.

Two sources of sound placed close to each other, are emitting progressive waves given by,
$y_1=4\sin 600\pi t$ and $y_2=5\sin 608\pi t$.
An observer located near these two sources of sound will hear:

1.	$4$ beats per second with intensity ratio $25:16$ between waxing and waning
2.	$8$ beats per second with intensity ratio $25:16$ between waxing and waning
3.	$8$ beats per second with intensity ratio $81:1$ between waxing and waning
4.	$4$ beats per second with intensity ratio $81:1$ between waxing and waning

22. Two waves are represented by the equations $y_1 = a\sin(\omega t+kx+0.57)~\text{m}$ and
$y_2 = a\cos(\omega t+kx)~\text{m},$ where $x$ is in meters and $t$ in seconds. The phase difference between them is:
1. $1.25$ rad
2. $1.57$ rad
3. $0.57$ rad
4. $1.0$ rad

23. Sound waves travel at $350$ m/s through warm air and at $3500$ m/s through brass. The wavelength of a $700$ Hz acoustic wave as it enters brass from warm air:

1.	increase by a factor of $20$.
2.	increase by a factor of $10$.
3.	decrease by a factor of $20$.
4.	decrease by a factor of $10$.

24.

A transverse wave is represented by $y=A\mathrm{sin}(\omega t-kx).$ At what value of the wavelength is the wave velocity equal to the maximum particle velocity?
1. $\pi A/2$
2. $\pi A$
3. $2\pi A$
4. $A$

25.

A tuning fork of frequency $512~\text{Hz}$ makes $4~\text{beats/s}$ with the vibrating string of a piano. The beat frequency decreases to $2~\text{beats/s}$ when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was:
1. $510~\text{Hz}$
2. $514~\text{Hz}$
3. $516~\text{Hz}$
4. $508~\text{Hz}$

26. A wave in a string has an amplitude of $2$ cm. The wave travels in the positive direction of the $x\text-$axis with a speed of $128~\text{m/s}$ and it is noted that $5$ complete waves fit in the $4$ m length of the string. The equation describing the wave is:
1. $y =(0.02~\text{m})\sin(7.85x+1005t)$
2. $y =(0.02~\text{m})\sin(15.7x-2010t)$
3. $y =(0.02~\text{m})\sin(15.7x+2010t)$
4. $y =(0.02~\text{m})\sin(7.85x-1005t)$

27.

The driver of a car travelling at a speed of 30 m/s towards a hill sounds a horn of frequency 600 Hz. If the velocity of sound in air is 330 m/s, the frequency of reflected sound as heard by the driver is:
1. 550 Hz
2. 555.5 Hz
3. 720 Hz
4. 500 Hz

28. Each of the two strings of lengths $51.6~\text{cm}$ and $49.1~\text{cm}$ is tensioned separately by $20~\text{N}$ of force. The mass per unit length of both strings is the same and equals $1~\text{g/m}.$ When both the strings vibrate simultaneously, the number of beats is:

1.	$5$	2.	$7$
3.	$8$	4.	$3$

29.

The wave described by $y=0.25\sin (10\pi x-2\pi t)$, where $x $ and $y$ are in metre and $t$ in second, is a wave travelling along the:

1.	–ve x-direction with frequency $1$ Hz
2.	+ve x-direction with frequency $\pi$ Hz and wavelength $\lambda=0.2$ m
3.	+ve x-direction with frequency $1$ Hz and wavelength $\lambda=0.2$ m
4.	–ve x-direction with amplitude $0.25$ m and wavelength $\lambda=0.2$ m

30.

Two sound waves with wavelengths $5.0~\text{m}$ and $5.5~\text{m}$, respectively, propagate in gas with a velocity of $330~\text{m/s}$. How many beats per second can we expect?
1. $12$
2. $0$
3. $1$
4. $6$

31.

A transverse wave propagating along the $x\text-$axis is represented by:
$y(x,t)=8.0\sin\left(0.5\pi x-4\pi t-\frac{\pi}{4}\right)$, where $x$ is in meters and $t$ in seconds. The speed of the wave is:
1. $4\pi$ m/s
2. $0.5$ m/s
3. $\frac{\pi}{4}$ m/s
4. $8$ m/s

32.

Which one of the following statements is true?

1.	Both light and sound waves in the air are transverse.
2.	The sound waves in the air are longitudinal while the light waves are transverse.
3.	Both light and sound waves in the air are longitudinal.
4.	Both light and sound waves can travel in a vacuum.

33. A tuning fork with a frequency of $800$ Hz produces resonance in a resonance column tube with the upper end open and the lower end closed by the water surface. Successive resonances are observed at lengths of $9.75$ cm, $31.25$ cm, and $52.75$ cm. The speed of the sound in the air is:

1.	$500$ m/s	2.	$156$ m/s
3.	$344$ m/s	4.	$172$ m/s

34.

In a guitar, two strings $A$ and $B$ made of same material are slightly out of tune and produce beats of frequency $6~\text{Hz}$. When tension in $B$ is slightly decreased, the beat frequency increases to $7~\text{Hz}$. If the frequency of $A$ is $530~\text{Hz}$, the original frequency of $B$ will be:

1.	$524~\text{Hz}$	2.	$536~\text{Hz}$
3.	$537~\text{Hz}$	4.	$523~\text{Hz}$

35.

The length of the string of a musical instrument is $90$ cm and has a fundamental frequency of $120$ Hz. Where should it be pressed to produce a fundamental frequency of $180$ Hz?

1.	$75$ cm	2.	$60$ cm
3.	$45$ cm	4.	$80$ cm

36.

A train moving at a speed of $220$ $m s^{- 1}$ towards a stationary object, emits a sound of frequency 1000 Hz. Some of the sound reaching the object gets reflected back to the train as an echo. The frequency of the echo as detected by the driver of the train is:(speed of sound in air is $330$ $m s^{- 1}$ )
1. 4000 Hz
2. 5000 Hz
3. 3000 Hz
4. 3500 Hz

37.

Two identical piano wires, kept under the same tension T, have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to the occurrence of 6 beats/s when both the wires oscillate together would be:
1. 0.01
2. 0.02
3. 0.03
4. 0.04

38.

For a wave $y=y_0 \sin (\omega t-k x)$, for what value of $\lambda$ is the maximum particle velocity equal to two times the wave velocity?
1. $\pi y_0$
2. $2\pi y_0$
3. $\pi y_0/2$
4. $4\pi y_0$

39.

Two stationary sources exist, each emitting waves of wavelength λ. If an observer moves from one source to the other with velocity u, then the number of beats heard by him is equal to:
1. $\frac{2 u}{λ}$
2. $\frac{u}{λ}$
3. $\sqrt{μ λ}$
4. $\frac{μ}{2 λ}$

40. A string is cut into three parts, having fundamental frequencies $n_1,n_2,$ and $n_3$respectively. The original fundamental frequency $n$ is related by the expression:
1. $\frac{1}{n}= \frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$
2. $n= n_1\times n_2\times n_3$
3. $n= n_1+ n_2+ n_3$
4. $n= \frac{n_1+ n_2+ n_3}{3}$

41.

The equations of two waves are given as x = acos(ωt + δ) and y = a cos (ωt + $α$ ), where δ = $α$ + $π$ /2, then the resultant wave can be represented by:
1. a circle (c.w)
2. a circle (a.c.w)
3. an ellipse (c.w)
4. an ellipse (a.c.w)

42. Two vibrating tuning forks produce progressive waves given by $Y_1 = 4 ~\mathrm{sin}~500 \pi \mathrm{t}$ and $Y_2 = 2 ~\mathrm{sin}~506 \pi \mathrm{t}$. The number of beats produced per minute is:

1.	$3$	2.	$360$
3.	$180$	4.	$60$

43. If a standing wave having $3$ nodes and $2$ antinodes is formed within $1.21~\mathring{A}$ distance, then the wavelength of the standing wave will be:
1. $1.21~\mathring{A}$
2. $2.42~\mathring{A}$
3. $0.605~\mathring{A}$
4. $4.84~\mathring{A}$

44. A point source emits sound equally in all directions in a non-absorbing medium. Two points, $P$ and $Q,$ are at distances of $2~\text m$ and $3~\text m,$ respectively, from the source. The ratio of the intensities of the waves at $P$ and $Q$ is:
1. $3:2$
2. $2:3$
3. $9:4$
4. $4:9$

45.

If a source moves perpendicularly to the listener, then the change in frequency will be:
1. 2n
2. n
3. n/2
4. Zero

46.

A car is moving towards a high cliff. The car driver sounds a horn at a frequency of 'f'. The reflected sound heard by the driver has a frequency of 2f. If 'v' is the velocity of sound, then the velocity of the car, in the same velocity units, will be:
1. v/3
2. v/4
3. v/2
4. v/ $\sqrt{2}$

47. A cylindrical tube $(L = 125~\text{cm})$ is resonant with a tuning fork at a frequency of $330~\text{Hz}$. If it is filled with water, then to get the resonance again, the minimum length of the water column will be: $(v_{\text{air}}= 330~\text{m/s})$

1.	$50~\text{cm}$	2.	$60~\text{cm}$
3.	$25~\text{cm}$	4.	$20~\text{cm}$

48.

The phase difference between two waves, represented by
$y_1= 10^{-6}\sin \left\{100t+\left(\frac{x}{50}\right) +0.5\right\}~\text{m}$
$y_2= 10^{-6}\cos \left\{100t+\left(\frac{x}{50}\right) \right\}~\text{m}$
where $x$ is expressed in metres and $t$ is expressed in seconds, is approximate:
1. $2.07~\text{radians}$
2. $0.5~\text{radians}$
3. $1.5~\text{radians}$
4. $1.07~\text{radians}$

49. If a wave is travelling in a positive $x\text-$direction with $A= 0.2~\text{m},$ $v=360~\text{m/s},$ and $\lambda= 60~\text{m},$ then the correct expression for the wave will be:

1.	${y}=0.2 \sin \left[2 \pi\left(6{t}+\frac{x}{60}\right)\right]$
2.	${y}=0.2 \sin \left[ \pi\left(6{t}+\frac{x}{60}\right)\right]$
3.	${y}=0.2 \sin \left[2 \pi\left(6{t}-\frac{x}{60}\right)\right]$
4.	$y=0.2 \sin \left[ \pi\left(6{t}-\frac{x}{60}\right)\right]$

50.

A whistle revolves in a circle with an angular speed ω = 20 rad/sec using a string of length 50 cm. If the frequency of sound from the whistle is 385 Hz, then what is the minimum frequency heard by an observer which is far away from the centre? (V_sound = 340 m/s)
1. 385 Hz
2. 374 Hz
3. 394 Hz
4. 333 Hz

51.

If the tension and diameter of a sonometer wire of fundamental frequency n are doubled and density is halved, then its fundamental frequency will become:
1. $\frac{n}{4}$
2. $\sqrt{2}$ $n$
3. n
4. $\frac{n}{\sqrt{2}}$

52.

Two waves have the following equations:
$x_{1}$ $=$ $a$ $\sin$ $(ω t$ $+$ $ϕ_{1})$
$x_{2}$ $=$ $a$ $\sin$ $(ω t$ $+$ $ϕ_{2})$
If in the resultant wave, the frequency and amplitude remain equal to the amplitude of superimposing waves, then the phase difference between them will be:
1. $\frac{π}{6}$
2. $\frac{2 π}{3}$
3. $\frac{π}{4}$
4. $\frac{π}{3}$

53.

An observer moves towards a stationary source of sound with a speed of 1/5th of the speed of sound. The wavelength and frequency of the source emitted are λ and f, respectively. The apparent frequency and wavelength recorded by the observer are, respectively:
1. 1.2f, 1.2λ
2. 1.2f, λ
3. f, 1.2λ
4. 0.8f, 0.8λ

54.

If the equation of a wave is represented by: $y=10^{-4}~ \mathrm{sin}\left(100t-\dfrac{x}{10}\right)~\text m,$ where $x $ is in meters and $t$ in seconds, then the velocity of the wave will be:

1.	$100$ m/s	2.	$4$ m/s
3.	$1000$ m/s	4.	$0$ m/s

55. If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is:

1.	$1:2$	2.	$1:1$
3.	$\sqrt{2}:1$	4.	$1:\sqrt{2}$

56.

A string of length $l$ is fixed at both ends and is vibrating in second harmonic. The amplitude at antinode is $2$ mm. The amplitude of a particle at a distance $l/8$ from the fixed end is:

1.	$2\sqrt2~\text{mm}$	2.	$4~\text{mm}$
3.	$\sqrt2~\text{mm}$	4.	$2\sqrt3~\text{mm}$

57. An organ pipe filled with a gas at $27^\circ \text{C}$ resonates at $400~\text{Hz}$ in its fundamental mode. If it is filled with the same gas at $90^\circ \text{C},$ the resonance frequency at the same mode will be:

1.	$420~\text{Hz}$	2.	$440~\text{Hz}$
3.	$484~\text{Hz}$	4.	$512~\text{Hz}$

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1.	\(13.2~\text{cm}\)	2.	\(8~\text{cm}\)
3.	\(12.5~\text{cm}\)	4.	\(16~\text{cm}\)

1.	\(100~\text{cm}\)	2.	\(150~\text{cm}\)
3.	\(200~\text{cm}\)	4.	\(66.7~\text{cm}\)

1.	\(\sqrt{\dfrac{m_1+m_2}{m_2}}\)	2.	\(\sqrt{\dfrac{m_2}{m_1}}\)
3.	\(\sqrt{\dfrac{m_1+m_2}{m_1}}\)	4.	\(\sqrt{\dfrac{m_1}{m_2}}\)

1.	\(8.0~\text{JK}^{-1}\text{mol}^{-1}\)	2.	\(7.5~\text{JK}^{-1}\text{mol}^{-1}\)
3.	\(7.0~\text{JK}^{-1}\text{mol}^{-1}\)	4.	\(8.5~\text{JK}^{-1}\text{mol}^{-1}\)

1.	\( 155~\text{Hz} \)	2.	\( 205~\text{Hz} \)
3.	\( 10.5~\text{Hz} \)	4.	\( 105~\text{Hz} \)

1.	\( \frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}\)
2.	\( \frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n_1}}+\frac{1}{\sqrt{n_2}}+\frac{1}{\sqrt{n_3}}\)
3.	\( \sqrt{n}=\sqrt{n_1}+\sqrt{n_2}+\sqrt{n_3}\)
4.	\( n=n_1+n_2+n_3\)

1.	\(246~\text{Hz}\)	2.	\(240~\text{Hz}\)
3.	\(260~\text{Hz}\)	4.	\(254~\text{Hz}\)

1.	\(y=\sin (2 \pi x-2 \pi t)\)	2.	\(y=\sin (10 \pi x-20 \pi t)\)
3.	\(y=\sin (2 \pi x+2 \pi t)\)	4.	\( y=\sin (x-2 t)\)

1.	\(\sqrt{\nu} = \sqrt{\nu_1}+\sqrt{\nu_2}+\sqrt{\nu_3}\)
2.	\(\nu = \nu_1+\nu_2+\nu_3\)
3.	\(\dfrac{1}{\nu} =\dfrac{1}{\nu_1} +\dfrac{1}{\nu_2}+\dfrac{1}{\nu_3}\)
4.	\(\dfrac{1}{\sqrt{\nu}} =\dfrac{1}{\sqrt{\nu_1}} +\dfrac{1}{\sqrt{\nu_2}}+\dfrac{1}{\sqrt{\nu_3}}\)

1.	\(4\) beats per second with intensity ratio \(25:16\) between waxing and waning
2.	\(8\) beats per second with intensity ratio \(25:16\) between waxing and waning
3.	\(8\) beats per second with intensity ratio \(81:1\) between waxing and waning
4.	\(4\) beats per second with intensity ratio \(81:1\) between waxing and waning

1.	\(20\) Hz	2.	\(30\) Hz
3.	\(40\) Hz	4.	\(10\) Hz

1.	\(L\)	2.	\(2L\)
3.	\(\dfrac{L}{2}\)	4.	\(4L\)

1.	\(1\)	2.	\(4\)
3.	\(3\)	4.	\(2\)

1.	\(330\) m/s	2.	\(339\) m/s
3.	\(350\) m/s	4.	\(300\) m/s

1.	increase by a factor of \(20\).
2.	increase by a factor of \(10\).
3.	decrease by a factor of \(20\).
4.	decrease by a factor of \(10\).

1.	–ve x-direction with frequency \(1\) Hz
2.	+ve x-direction with frequency \(\pi\) Hz and wavelength \(\lambda=0.2\) m
3.	+ve x-direction with frequency \(1\) Hz and wavelength \(\lambda=0.2\) m
4.	–ve x-direction with amplitude \(0.25\) m and wavelength \(\lambda=0.2\) m

1.	\(524~\text{Hz}\)	2.	\(536~\text{Hz}\)
3.	\(537~\text{Hz}\)	4.	\(523~\text{Hz}\)

1.	\(50~\text{cm}\)	2.	\(60~\text{cm}\)
3.	\(25~\text{cm}\)	4.	\(20~\text{cm}\)

1.	\({y}=0.2 \sin \left[2 \pi\left(6{t}+\frac{x}{60}\right)\right]\)
2.	\({y}=0.2 \sin \left[ \pi\left(6{t}+\frac{x}{60}\right)\right]\)
3.	\({y}=0.2 \sin \left[2 \pi\left(6{t}-\frac{x}{60}\right)\right]\)
4.	\(y=0.2 \sin \left[ \pi\left(6{t}-\frac{x}{60}\right)\right]\)

1.	\(2\sqrt2~\text{mm}\)	2.	\(4~\text{mm}\)
3.	\(\sqrt2~\text{mm}\)	4.	\(2\sqrt3~\text{mm}\)

1.	\(420~\text{Hz}\)	2.	\(440~\text{Hz}\)
3.	\(484~\text{Hz}\)	4.	\(512~\text{Hz}\)

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