Waves

Two sources P and Q produce notes of frequency 660 Hz each. A listener moves from P to Q with a speed of 1 m s-1. If the speed of sound is 330 m/s, then the number of beats heard by the listener per second will be

1. 4
2. 8
3. 2
4. zero

The equation of a simple harmonic wave is given by y = 3 2(50t - x), where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is

1. 2
2. 32
3. 3
4. 23

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 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. 3500 Hz
2. 4000 Hz
3. 5000 Hz
4. 3000 Hz

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