Waves · Question 24

A wave travelling in the +ve x-direction having displacement along y-direction as 1 m, wavelength 2 m and frequency of 1 Hz is represented by

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

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. 240 Hz
2. 260 Hz
3. 254 Hz
4. 246 Hz

The length of the wire between two ends of a sonometer is 100 cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio 1 : 3 : 5.

1. 150023 cm, 50023 cm
2. 150023 cm, 30023 cm
3. 30023 cm, 150023 cm
4. 150023 cm, 200023 cm

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