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1.

The isothermal elasticity of a medium is ${\mathrm{E}}_{\mathrm{i}}$ and the adiabatic elasticity in ${\mathrm{E}}_{\mathrm{a}}$. The velocity of sound in the medium is proportional to
1.  ${\mathrm{E}}_{\mathrm{i}}$
2.  ${\mathrm{E}}_{\mathrm{a}}$
3.  $\sqrt{{\mathrm{E}}_{\mathrm{i}}}$
4.  $\sqrt{{\mathrm{E}}_{\mathrm{a}}}$

2.

A source of sound moves away with the velocity of sound from a stationary observer. The frequency of the sound heard by the observer:
1. remains the same
2. is doubled
3. is halved
4. becomes infinity
 

3.

The equation of a wave pulse travelling along x-axis is given by $y=\frac{30}{2+{\left(x-20t\right)}^2}$, x and y are in meters and t is in seconds. The amplitude of the wave pulse is 
1.  5 m
2.  20 m
3.  15 m
4.  30 m

4. The equation of a standing wave in a string is \(y = (200~\text{m})\sin\left(\frac{2\pi}{50}x\right)\cos\left(\frac{2\pi}{0.01}t\right)\) where \(x\) is in metres and \(t\) is in seconds. At the position of antinode, how many times does the distance of a string particle become \(200~\text{m}\) from its mean position in one second?

1.	\(100~\text{times}\)	2.	\(50~\text{times}\)
3.	\(200~\text{times}\)	4.	\(400~\text{times}\)

5. Eleven tuning forks are arranged in increasing order of frequency in such a way that any two consecutive tuning forks produce \(4\) beats per second. The highest frequency is twice that of the lowest. The highest and the lowest frequencies (in Hz) are, respectively:

1.	\(100~\text{and}~50\)	2.	\(44~\text{and}~22\)
3.	\(80~\text{and}~40\)	4.	\(72~\text{and}~30\)

6.

The sound intensity level at a point 10 m away from a point source is 20dB, then the sound level at a distance 1m from the same source would be
1. 40 dB
2. 30 dB
3. 200 dB
4. 100 dB

7.

In the phenomenon of interference of sound by two coherent sources if difference of intensity at maxima to intensity at minima is 20dB, then the ratio of intensities of the two sources is
1.  $\frac{121}{81}$
2.  $\frac{11}{9}$
3.  $\frac{101}{99}$
4.  $\frac{10}{1}$

8. The two nearest harmonics of a tube close at one end and open at the other end are \(220~\text{Hz}\) and \(260~\text{Hz}\). What is the fundamental frequency of the system?

1.	\(10~\text{Hz}\)	2.	\(20~\text{Hz}\)
3.	\(30~\text{Hz}\)	4.	\(40~\text{Hz}\)

9.

Two cars moving in opposite directions approach each other with speed of 22m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [velocity of sound 340m/s]
1. 350Hz
2. 361Hz
3. 411Hz
4. 448Hz

10.

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L metre long. The length of the open pipe will be
1. L         
2. 2L
3. L/2     
4. 4L

11.

A siren emitting a sound of frequency 800 Hz moves away from an observer towards a cliff at a speed of $15{\mathrm{ms}}^{-1}$. The frequency of sound that the observer hears in the echo reflected from the cliff will be:
(Take, velocity of sound in air=$330$ ${\mathrm{ms}}^{-1}$)
1. 800 Hz
2. 838 Hz
3. 885 HZ
4. 765 Hz

12.

A uniform rope of length \(L\) and mass \(m_1\) hangs vertically from a rigid support. A block of mass \(m_2\) is attached to the free end of the ropes. A transverse pulse of wavelength \(\lambda_1\) is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \(\lambda_2\). The ratio \(\dfrac{\lambda_2}{\lambda_1}\) is:
1. \(\sqrt{\dfrac{m_1+m_2}{m_1}}\)
2. \(\sqrt{\dfrac{m_2}{m_1}}\)
3. \(\sqrt{\dfrac{m_1+m_2}{m_2}}\)
4. \(\sqrt{\dfrac{m_1}{m_2}}\)

13. The number of possible natural oscillations of the air column in a pipe closed at one end of a length of \(85~\text{cm}\) whose frequencies lie below \(1250~\text{Hz}\) is: (velocity of sound \(340~\text{ms}^{-1}\))

1.	\(4\)	2.	\(5\)
3.	\(7\)	4.	\(6\)

14.

When a string is divided into three segments of lengths $l_1, l_2 and l_3,$ the fundamental frequencies of these three segments are $v_1, v_2 and v_3$ 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. $\frac{1}{v}=\frac{1}{v_1}+\frac{{\displaystyle 1}}{{\displaystyle v_2}}+\frac{{\displaystyle 1}}{{\displaystyle v_3}}$
4. $\frac{1}{\sqrt{v}}=\frac{1}{\sqrt{v_1}}+\frac{{\displaystyle 1}}{{\displaystyle \sqrt{v_2}}}+\frac{{\displaystyle 1}}{{\displaystyle \sqrt{v_3}}}$

15.

Two waves are represented by the equations ${\mathrm{y}}_1=\mathrm{a} \sin (\mathrm{\omega t}+\mathrm{kx}+0.57)\mathrm{m}$ and ${\mathrm{y}}_2=\mathrm{a} \cos (\mathrm{\omega t}+\mathrm{kx})\mathrm{m}$, where x is in metre and t in second. The phase difference between them is?
1. 1.25 rad
2. 1.57 rad
3. 0.57 rad
4. 1.0 rad