Two sources are at a finite distance apart. They emit sounds of wavelength $\mathrm{\lambda }$. An observer situated between them on line joining approaches one source with speed u. Then the number of beats heard per second by observer will be:

1. $\frac{2u}{\lambda }$

2. $\frac{u}{\lambda }$

3. $\frac{u}{2\lambda }$

4. $\frac{\lambda }{u}$

The frequency of a vibrating wire is n. If tension is doubled, density is halved and diameter is doubled, then new frequency will be

1. n

2. $\frac{n}{\sqrt{2}}$

3. 2n

4. 4n

An observer moves towards a stationary source of sound with a speed 1/5th of the speed of sound. The wavelength and frequency of the sound emitted are $\mathrm{\lambda }<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>\mathrm{f}$ respectively. The apparent frequency and wavelength recorded by the observer are respectively -

1. $1.2\mathrm{f},<mspace\; width="1em"></mspace>1.2\mathrm{\lambda }$

2. $1.2\mathrm{f},<mspace\; width="1em"></mspace>\mathrm{\lambda }$

3. $\mathrm{f},<mspace\; width="1em"></mspace>1.2\mathrm{\lambda }$

4. $0.8\mathrm{f},<mspace\; width="1em"></mspace>0.8\mathrm{\lambda }$

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. $\frac{v}{\sqrt{2}}$

Two vibrating tuning forks produce progressive waves given by ${\mathrm{y}}_1=4\sin <mspace\; width="1em"></mspace>500\mathrm{\pi t}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{y}}_2=2\sin 506\mathrm{\pi t}$. Number of beats produced per minute in.

1. 3

2. 360

3. 180

4. 60

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.

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

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 transverse wave is represented by y=A $\sin <mspace\; width="1em"></mspace>(\omega t-kx)$. 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. $2\mathrm{\pi A}$

Two waves are represented by the equations

   ${\mathrm{y}}_1=\mathrm{asin}(\mathrm{\omega t}+\mathrm{kx}+0.57)\mathrm{m}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{y}}_2=\mathrm{acos}(\mathrm{\omega t}+\mathrm{kx})\mathrm{m}$

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