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

A speed motorcyclist sees a traffic jam ahead of him. He slows down to 36km/h. He finds that traffic has eased and a car moving in front of him at 18km/h is honking at a frequency of 1392Hz. If the speed of sound is 343m/s, the frequency of the honk as heard by him will be 
1. 1332Hz
2. 1372Hz
3. 1412Hz
4. 1454Hz 

A wave travelling in the positive x-direction having maximum displacement along y-direction as 1m, wavelength 2π m and frequency of 1/π Hz is represented by

(1) y=sin(x-2t)

(2) y=sin(2πx-2πt)

(3) y=sin(10πx-20πt)

(4) y=sin(2πx+2πt)

If we study the vibration of a pipe open at both ends. then the following statements is not true

(1) Open end will be anti-node

(2) Odd harmonics of the fundamental frequency will be generated

(3) All harmonics of the fundamental frequency will be generated

(4) Pressure change will be maximum at both ends