A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of \(27^{\circ}\mathrm{C}\), to successive resonances are produced at 20 cm and 73 cm column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at \(27^{\circ}\mathrm{C}\) is:

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 \(20~\text{cm}\), the length of the open organ pipe is:
1. \(13.2~\text{cm}\)
2. \(8~\text{cm}\)
3. \(12.5~\text{cm}\)
4. \(16~\text{cm}\)

The two nearest harmonics of a tube close at one end and open at the other end are 220Hz and 260Hz. What is the fundamental frequency of the system?

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

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L meter long. The length of the open pipe will be:

1.  L

2.  2L

3.  L/2

4.  4L

Three sound waves of equal amplitudes have frequencies of \((n-1),~n,\) and \((n+1).\) They superimpose to give beats. The number of beats produced per second will be: