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