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

A wave travelling in the +ve x-direction having maximum displacement along y-direction as 1 m, wavelength $2\pi m$ and frequency of $\frac{1}{\mathrm{\pi }}$ Hz, is represented by:

$1. y=\sin \left(2\pi x-2\pi t\right)$
2. y=sin10πx-20πt
3. y=sin2πx+2πt
4. y=sinx-2t

Two sources of sound placed close to each other, are emitting progressive waves given by,
 $y_1$=4sin600$\pi$t and $y_2$=5sin608$\pi$t
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 waves are represented by the equations $y_1=a \sin (\omega t+kx+0.57) m$ and $y_2=a\cos (\omega t+kx) m$, where x is in metres and t in seconds. The phase difference between them is:
1. 1.25 rad
2. 1.57 rad
3. 0.57 rad
4. 1.0 rad

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.  increase by a factor of 20

2.  increase by a factor of 10

3.  decrease by a factor of 20

4.  decrease by a factor of 10

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

1. $\pi$A/2

2. $\pi$A

3. 2$\pi$A

4. A

A tuning fork of frequency 512 Hz makes 4 beats/s with the vibrating string of a piano. The beat frequency decreases to 2 beats/s 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

A wave in a string has an amplitude of 2 cm. The wave travels in the positive direction of the 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(7.85x+1005t)
2. y = (0.02)m sin(15.7x -2010t)
3. y = (0.02)m sin(15.7x+2010t)
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 the driver is:

1. 550 Hz

2. 555.5 Hz

3. 720 Hz

4. 500 Hz

Each of the two strings of lengths 51.6 cm and 49.1 cm is tensioned separately by 20 N of force. The mass per unit length of both the strings is the same and equals 1 g/m. When both the strings vibrate simultaneously, the number of beats is:

1. 5

2. 7

3. 8

4. 3