Two waves are represented by the equations

   ${\mathrm{y}}_1=\mathrm{asin}(\mathrm{\omega t}+\mathrm{kx}+0.57)\mathrm{m} \mathrm{and} {\mathrm{y}}_2=\mathrm{acos}(\mathrm{\omega t}+\mathrm{kx})\mathrm{m}$

where x is in m and t in s. The phase difference between them is

1. 0.57 rad

2. 1.0 rad

3. 1.25 rad

4. 1.57 rad

When a string is divided into three segments of length ${\mathrm{l}}_1, {\mathrm{l}}_2 \mathrm{and} {\mathrm{l}}_3$, the fundamental frequencies of these three segments are ${\mathrm{v}}_1, {\mathrm{v}}_2 \mathrm{and} {\mathrm{v}}_3$ respectively. The original fundamental frequency (v) of the string is

1. $\sqrt{v}=\sqrt{v_1}+\sqrt{v_2}+\sqrt{v_3}$

2. $v=v_1+v_2+v_3$

3. $\frac{1}{v}=\frac{1}{v_1}+\frac{1}{v_2}+\frac{1}{v_3}$

4. $\frac{1}{\sqrt{v}}=\frac{1}{\sqrt{v_1}}+\frac{1}{\sqrt{v_2}}+\frac{1}{\sqrt{v_3}}$

A train moving at a speed of 220 m ${\mathrm{s}}^{-1}$ towards a stationary object emits a sound of frequency 1000 Hz. Some of the sound reaching of 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 ${\mathrm{s}}^{-1}$)

1. 5000Hz

2. 3000Hz

3. 3500Hz

4. 4000Hz

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is

1. 12.5 cm

2. 8 cm

3. 13.2 cm

4. 16 cm

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

1. A

2. $\frac{\mathrm{\pi A}}{2}$

3. $\mathrm{\pi A}$

4. $2\mathrm{\pi A}$

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 ${\mathrm{m}}^{-1}$. 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 amplitude of 2 cm. The wave travels in the +ve direction of x-axis with a speed of 128 m ${\mathrm{s}}^{-1}$ and it is noted that 5 complete waves are formed in 4m length of the string. The equation describing the wave is

1. y=(0.02)sin (15.7x - 2010t)m

2. y = (0.02) sin (15.7x + 2010t)m

3. y = (0.02) sin (7.85x - 1005t)m

4. y = (0.02) sin (7.85x + 1005t)m

Which one of the following statement is true:

1. Both light and sound waves in air are transverse.

2. The sound waves in air are longitudinal while the light wave are transverse.

3. Both light and sound waves in air are longitudinal.

4. Both light and sound waves can travel in vacuum.

Two vibrating tuning forks produce progressive waves given by ${\mathrm{y}}_1=4\sin 500\mathrm{\pi t} \mathrm{and} {\mathrm{y}}_2=2\sin 506\mathrm{\pi t}$. Number of beats produced per minute in.

1. 3

2. 360

3. 180

4. 60

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

1. $\frac{v}{3}$

2. $\frac{v}{4}$

3. $\frac{v}{2}$

4. $\frac{v}{\sqrt{2}}$