Waves

When a string is divided into three segments of lengths l1, l2 and l3, the fundamental frequencies of these three segments are 1, 2 and 3 respectively. The original fundamental frequency ( ) of the string is

1. = 1 + 2 + 3
2. = 1 + 2 + 3
3. 1 = 1 1 + 1 2 + 1 3
4. 1 = 1 1 + 1 2 + 1 3

Two sources of sound placed close to each other, are emitting progressive waves given by y1 = 4 600 and y2 = 5 608 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.

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 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

Two waves are represented by the equations y1 = a sin( t + kx + 0.57) m and y2 = a cos( t + kx) m, where x is in metre and t in second. The phase difference between them is

1. 1.0 radian
2. 1.25 radian
3. 1.57 radian
4. 0.57 radian

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. decrease by a factor 10
2. increase by a factor 20
3. increase by a factor 10
4. decrease by a factor 20

A transverse wave is represented by y = A ( - kx). For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

1. /2
3. 2
4. A

A tuning fork of frequency 512 Hz makes 4 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per sec when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

1. 510 Hz
2. 514 Hz
3. 516 Hz
4. 508 Hz

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. When both the strings vibrate simultaneously the number of beats is

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

A wave in a string has an amplitude of 2 cm. The wave travels in the +ve direction of x axis with a speed of 128 m/s and it is noted that 5 complete waves fit in 4 m length of the string. The equation describing the wave is

1. y = (0.02) m sin (15.7x - 2010t)
2. y = (0.02) m sin (15.7x + 2010t)
3. y = (0.02) m sin (7.85x - 1005t)
4. y = (0.02) m sin (7.85x + 1005t)

The driver of a car travelling with speed 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 driver is

1. 555.5 Hz
2. 720 Hz
3. 500 Hz
4. 550 Hz

Two periodic waves of intensities I1 and I2 pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

1. ( I1 - I2 )2
2. 2 (I1 + I2 )
3. I1 + I2
4. ( I1 + I2 )2

The wave described by y = 0.25 sin(10 x - 2 t), where x and y are in metres and t in seconds, is a wave travelling along the

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

Two vibrating tuning forks produce waves given by y1 = 4 500 t and y2 = 2 506 t. Number of beats produced per minute is

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

Two sound waves with wavelengths 5.0 m and 5.5 m respectively, each propagate in a gas with velocity 330 m/s. We expect the following number of beats per second.

1. 6
2. 12
3. 0
4. 1

The time of reverberation of a room A is one second. What will be the time (in seconds) of reverberation of a room, having all the dimensions double of those of room A?

1. 1
2. 2
3. 4
4. 1/2

A transverse wave propagating along x-axis is represented by y(x, t) = 8.0 (0.5 x - 4 t - /4) where x is in metres and t is in seconds. The speed of the wave is

1. 8 m/s
2. 4 m/s
3. 0.5 m/s
4. /4 m/s

Which one of the following statements is true?

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

A point source emits sound equally in all directions in a non-absorbing medium. Two points P and Q are at distances of 2 m and 3 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

The phase difference between two waves represented by y1 = 10-6 [100t + (x/50) + 0.5] m y2 = 10-6 [100t + (x/50)] m, where x is expressed in metres and t is expressed in seconds, is approximately

1. 1.07 radians
2. 2.07 radians
3. 0.5 radians
4. 1.5 radians

A car is moving towards a high cliff. The driver sounds a horn of frequency f. The reflected sound heard by the driver has frequency 2f. If v is the velocity of sound, then the velocity of the car, in the same velocity units, will be

1. v/ 2
2. v/3
3. v/4
4. v/2

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 source emitted are and f respectively. The apparent frequency and wavelength recorded by the observer are respectively

1. 1.2f, 1.2
2. 1.2f,
3. f, 1.2
4. 0.8f, 0.8

A wave travelling in positive X-direction with a = 0.2 m, velocity = 360 m s-1 and = 60 m, then correct expression for the wave is

1. y = 0.2 [2 (6t + x60 ) ]
2. y = 0.2 [ (6t + x60 ) ]
3. y = 0.2 [2 (6t - x60 ) ]
4. y = 0.2 [ (6t - x60 ) ]

A whistle revolves in a circle with angular speed = 20 rad/s 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 (velocity of sound = 340 m/s)

1. 385 Hz
2. 374 Hz
3. 394 Hz
4. 333 Hz

The equation of a wave is represented by y = 10-4 (100t - x10 ) m, then the velocity of wave will be

1. 100 m/s
2. 4 m/s
3. 1000 m/s
4. 10 m/s

Two waves having equation x1 = a ( t - kx + 1), x2 = a ( t - kx + 2). If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves, the phase difference between them is

1. 6
2. 2 3
3. 4
4. 3

If the tension and diameter of a sonometer wire of fundamental frequency n is doubled and density is halved then its fundamental frequency will become

1. n4
2. 2n
3. n
4. n 2

A string is cut into three parts, having fundamental frequencies n1, n2, n3 respectively. Then original fundamental frequency n related by the expression as

1. 1n = 1n1 + 1n2 + 1n3
2. n = n1 n2 n3
3. n = n1 + n2 + n3
4. n = n1 + n2 + n33

Two stationary sources each emit waves of wavelength . An observer moves from one source to the other with velocity u. Then the number of beats heard by him is

1. 2u
2. u
3. u
4. u2