Question

A tuning fork vibrating at 300 Hz, initially in air, is then placed in a trough of water. The ratio of the wavelength of the sound waves produced in air to that in water is (Given that the velocity of sound in water and in air at that place are 1500 m/s and 350 m/s respectively):

• A. 1:1
• B. 37:23
• C. 30:7
• D. 7:30
• E. 23:37

Hint:

The wavelength of a wave depends directly on the velocity of the medium and inversely on the frequency.

Answer 1

The Correct Option is D

The wavelength \( \lambda \) of a wave is given by \( \lambda = \frac{v}{f} \). 
For air and water: \[ \lambda_{{air}} = \frac{350 { m/s}}{300 { Hz}} = \frac{7}{6} { m}, \quad \lambda_{{water}} = \frac{1500 { m/s}}{300 { Hz}} = 5 { m} \] \[ {Ratio} = \frac{\lambda_{{air}}}{\lambda_{{water}}} = \frac{\frac{7}{6}}{5} = \frac{7}{30} \]