Bottom of Pyramid - Test # 25- Waves

A tuning fork and sonometer give 5 beats per second when the length of the wire is 1 m and 1.05 m respectively. The frequency of fork is -
1. 210 Hz
2. 205 Hz
3. 410 Hz
4. 420 Hz

2. The two nearest harmonics of a tube close at one end and open at the other end are $220~\text{Hz}$ and $260~\text{Hz}$. What is the fundamental frequency of the system?

1.	$10~\text{Hz}$	2.	$20~\text{Hz}$
3.	$30~\text{Hz}$	4.	$40~\text{Hz}$

A wave travelling in the positive x-direction having maximum displacement along y-direction as 1m, wavelength 2π m and frequency of 1/π Hz is represented by
1. y=sin(x-2t)
2. y=sin(2πx-2πt)
3. y=sin(10πx-20πt)
4. y=sin(2πx+2πt)

A source of unknown frequency gives 4 beats/s when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency 513 Hz. The unknown frequency is
1. 254 Hz
2. 246 Hz
3. 240 Hz
4. 260 Hz

Two sources of sound placed close to each other, are emitting progressive waves given by
$y_{1}$ =4 sin 600 $πt$ and $y_{2}$ =5 sin 608 $πt$
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 waxing and waning

A train moving at a speed of 220 ${ms}^{- 1}$ 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 ${ms}^{- 1}$ )
1. 3500Hz
2. 4000Hz
3. 5000Hz
4. 3000Hz

Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is :
(1)zero
(2) $\frac{2 π}{3}$
(3) $π$
(4) $\frac{π}{6}$

A tuning fork makes 256 vibrations per second in air. When the velocity of sound is 330 m/s, then the wavelength of the tone emitted is :
1. 0.56 m
2. 0.89 m
3. 1.11 m
4. 1.29 m

The phase difference between two points separated by 1m in a wave of frequency 120 Hz is 90°. The wave velocity is :
1. 180 m/s
2. 240 m/s
3. 480 m/s
4. 720 m/s

10.

The echo of a gunshot is heard 8 sec. after the gun is fired. How far from him is the surface that reflects the sound? (velocity of sound in air = 350 m/s) :
1. 1400 m
2. 2800 m
3. 700 m
4. 350 m

11.

The velocity of sound in air is:

1.	faster in dry air than in moist air.
2.	directly proportional to the pressure.
3.	directly proportional to temperature.
4.	independent of the pressure of air.

12.

The frequency of a sound wave is n and its velocity is v. If the frequency is increased to 4n, the velocity of the wave will be
(1) v
(2) 2v
(3) 4v
(4) v/4

13.

The type of waves that can be propagated through solid is :
(1) Transverse
(2) Longitudinal
(3) Both (1) and (2)
(4) None of these

14.

A wave of the frequency of 500 Hz has a velocity of 360 m/sec. The distance between two nearest points 60° out of phase is :
(1) 0.6 cm
(2) 12 cm
(3) 60 cm
(4) 120 cm

15.

A wavelength 0.60 cm is produced in air and it travels at a speed of 300 ms^–1. It will be an
(1) Audible wave
(2) Infrasonic wave
(3) Ultrasonic wave
(4) None of the above

16.

An observer standing near the seashore observes 54 waves per minute. If the wavelength of the water wave is 10m then the velocity of a water wave is :
(1) 540 ms^-1
(2) 5.4 ms^-1
(3) 0.184 ms^-1
(4) 9 ms^-1

17.

The equation of a wave is $y = 2 \sin π (0 .5 x - 200 t)$ , where x and y are expressed in cm and t in sec. The wave velocity is :
1. 100 cm/sec
2. 200 cm/sec
3. 300 cm/sec
4. 400 cm/sec

18.

Two waves are given by $y_{1} = a \sin (ω t - k x)$ and $y_{2} = a \cos (ω t - k x)$ . The phase difference between the two waves is :
(1) $\frac{π}{4}$
(2) π
(3) $\frac{π}{8}$
(4) $\frac{π}{2}$

19. The displacement of a particle is given by $y = 5\times 10^{-4}\sin\left(100t-50x\right),$ where $x$ is in metres and $t$ is in seconds. The velocity of the wave is:
1. $5000~\text{m/s}$
2. $2~\text{m/s}$
3. $0.5~\text{m/s}$
4. $300~\text{m/s}$

20. The wave equations of two particles are given by $y_1=a\sin(\omega t-kx), y_2 = a \sin(kx+\omega t),$ then:

1.	they are moving in the opposite direction.
2.	the phase between them is $90^{\circ}$.
3.	the phase between them is $45^{\circ}$.
4.	the phase between them is $0^{\circ}$.

21. The equation of a progressive wave is given by $y = 4\sin\left\{ \pi\left(\frac{t}{5}-\frac{x}{9}\right)+\frac{\pi}{6}\right\}$, where $x$ and $y$ are in metres and $t$ in seconds.
Which of the following is correct?
1. $v = 5~\text{m/s}$
2. $\lambda = 18~\text{m}$
3. $A = 0.04~\text{m}$
4. $\nu= 50~\text{Hz}$

22.

Two waves of frequencies 20 Hz and 30 Hz travel out from a common point. The phase difference between them after 0.6 sec is :
(1) Zero
(2) $\frac{π}{2}$
(3) π
(4) $\frac{3 π}{4}$

23.

The equation of progressive wave is $y = a \sin (200 t - x)$ . where x is in meter and t is in second. The velocity of wave is :
(1) 200 m/sec
(2) 100 m/sec
(3) 50 m/sec
(4) None of these

24.

A wave travelling in positive X-direction with A = 0.2 m has a velocity of 360 m/sec. if λ = 60 m, then the correct expression for the wave is :
(1) $y = 0 .2 \sin [2 π (6 t + \frac{x}{60})]$
(2) $y = 0 .2 \sin [π (6 t + \frac{x}{60})]$
(3) $y = 0 .2 \sin [2 π (6 t - \frac{x}{60})]$
(4) $y = 0 .2 \sin [π (6 t - \frac{x}{60})]$

25.

A transverse progressive wave on a stretched string has a velocity of 10 ms^–1 and a frequency of 100 Hz. The phase difference between two particles of the string which are 2.5 cm apart will be :
(1) $\frac{π}{8}$
(2) $\frac{π}{4}$
(3) $\frac{3 π}{8}$
(4) $\frac{π}{2}$

26.

The intensity ratio of the two waves is 1 : 16. The ratio of their amplitudes is
(1) 1 : 16
(2) 1 : 4
(3) 4 : 1
(4) 2 : 1

27.

A tuning fork sounded together with a tuning fork of frequency 256 Hz emits two beats. On loading the tuning fork of frequency 256 Hz with wax, the number of beats heard are 1 per second. The frequency of the other tuning fork is :
(1) 257
(2) 258
(3) 256
(4) 254

28. Tuning fork $F_1$ has a frequency of $256~\text{Hz}$ and it is observed to produce $6$ beats/second with another tuning fork $F_2$. When $F_2$ is loaded with wax, it still produces $6$ beats/second with $F_1$. The frequency of $F_2$ before loading was:
1. $253~\text{Hz}$
2. $262~\text{Hz}$
3. $250~\text{Hz}$
4. $259~\text{Hz}$

29.

Two vibrating tuning forks produce progressive waves given by $Y_{1} = 4 \sin 500 π t$ and $Y_{2} = 2 \sin 506 π t .$ Number of beats produced per minute is :
(1) 360
(2) 180
(3) 3
(4) 60

30.

Standing waves are produced in a 10 m long stretched string. If the string vibrates in 5 segments and the wave velocity is 20 m/s, the frequency is :
(1) 2 Hz
(2) 4 Hz
(3) 5 Hz
(4) 10 Hz

31.

The correct graph between the frequency n and square root of density (ρ) of wire, keeping its length, radius and tension constant, is :
(1)
(2)
(3)
(4)

32.

The displacement-time graphs for two sound waves A and B are shown in the figure, then the ratio of their intensities I_A/I_B is equal to :

1. 1 : 4
2. 1 : 16
3. 1 : 2
4. 1 : 1

33.

In a sinusoidal wave, the time required for a particular point, to move from maximum displacement to zero displacement is 0.170 s. The frequency of the wave is
1. 1.47 Hz
2. 0.36 Hz
3. 0.73 Hz
4. 2.93 Hz

34.

A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance 1.21 $\overset{°}{A}$ between them. The wavelength of the standing wave is
1. 1.21 $\overset{°}{A}$
2. 1.42 $\overset{°}{A}$
3. 6.05 $\overset{°}{A}$
4. 3.63 $\overset{°}{A}$

35.

Two sources are at a finite distance apart. They emit sounds of wavelength $λ$ . An observer situated between them on line joining approaches one source with speed u. Then the number of beats heard per second by observer will be:
1. $\frac{2 u}{λ}$
2. $\frac{u}{λ}$
3. $\frac{u}{2 λ}$
4. $\frac{λ}{u}$

36.

The frequency of a vibrating wire is n. If tension is doubled, density is halved and diameter is doubled, then new frequency will be
1. n
2. $\frac{n}{\sqrt{2}}$
3. 2n
4. 4n

37.

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

38.

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

39.

Which one of the following statement is true:
1. Both light and sound waves in air are transverse.
2. The sound waves in air are longitudinal while the light wave are transverse.
3. Both light and sound waves in air are longitudinal.
4. Both light and sound waves can travel in vacuum.

40.

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

41.

Each of the two strings of length 51.6 cm and 49.1 cm are tensioned separately by 20 N force. Mass per unit length of both the strings is same and equal to 1 g $m^{- 1}$ . When both the strings vibrate simultaneously the number of beats is
1. 7
2. 8
3. 3
4. 5

42.

A transverse wave is represented by y=A $\sin (ω t - k x)$ . For what value of the wavelength is the wave velocity equal to the maximum particle velocity?
1. A
2. $\frac{πA}{2}$
3. $πA$
4. $2 πA$

43.

Two waves are represented by the equations
$y_{1} = asin (ωt + kx + 0.57) m and y_{2} = acos (ωt + kx) m$
where x is in m and t in s. The phase difference between them is
1. 0.57 rad
2. 1.0 rad
3. 1.25 rad
4. 1.57 rad

44.

When a string is divided into three segments of length $l_{1}, l_{2} and l_{3}$ , the fundamental frequencies of these three segments are $v_{1}, v_{2} and v_{3}$ respectively. The original fundamental frequency (v) of the string is
1. $\sqrt{v} = \sqrt{v_{1}} + \sqrt{v_{2}} + \sqrt{v_{3}}$
2. $v = v_{1} + v_{2} + v_{3}$
3. $\frac{1}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}} + \frac{1}{v_{3}}$
4. $\frac{1}{\sqrt{v}} = \frac{1}{\sqrt{v_{1}}} + \frac{1}{\sqrt{v_{2}}} + \frac{1}{\sqrt{v_{3}}}$

45.

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 cm, the length of the open organ pipe is
1. 12.5 cm
2. 8 cm
3. 13.2 cm
4. 16 cm

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1.	\(10~\text{Hz}\)	2.	\(20~\text{Hz}\)
3.	\(30~\text{Hz}\)	4.	\(40~\text{Hz}\)

1.	they are moving in the opposite direction.
2.	the phase between them is \(90^{\circ}\).
3.	the phase between them is \(45^{\circ}\).
4.	the phase between them is \(0^{\circ}\).

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