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

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

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

An air column, closed at one end and open at the other, resonates with a running fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tunning fork is

(1) 1OO cm

(2) 150 cm

(3) 200 cm

(4) 66.7cm 

A uniform rope of length L and mass m₁ hangs vertically from a rigid support. A block of mass m₂ is attached to the free end of the ropes. A transverse pulse of wavelength λ₁ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is λ₂. The ratio λ₂/λ₁ is-

1. $\sqrt{\frac{m_1+m_2}{m_2}}$

2. $\sqrt{\frac{m_2}{m_1}}$

3. $\sqrt{\frac{m_1+m_2}{m_1}}$

4. $\sqrt{\frac{m_1}{m_2}}$

A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 ms^-1 at an angle of 60° with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound to air 330 ms^-1), is

(1) 100 Hz

(2) 103Hz

(3) 106 Hz

(4) 97 Hz

4.0 g of a gas occupies 22.4 L at NTP. The specific heat capacity of the gas at constant volume is 5.0 J K^-1mol^-1. If the speed of sound in this gas at NTP is$952 m{s}^{-1}$, then the heat capacity at constant pressure is: (Take gas constant R=8.3 JK^-1mol^-1)

(1) 8.0 JK^-1mol^-1
 

(2) 7.5 JK^-1mol^-1
 

(3) 7.0 JK^-1mol^-1
 

(4) 8.5 JK^-1mol^-1

If n₁, n₂ and n₃ are, are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by

(1) 1/n=1/n₁+1/n₂+1/n₃

(2) 1/√n=1/√n₁+1/√n₂+1/√n₃

(3) √n=√n₁+√n₂+√n₃

(4) n=n₁+n₂+n₃