Answer :

Given:

Frequency of tuning fork = 512 Hz

Water level below open end = 17 cm

The water acts as a reflective surface for the wave, therefore the tube behaves like an organ pipe. When the water level is such that the frequency of the wave matches the resonant frequency of the organ pipe the maximum sound is heard.

(a) Since at 17 cm maximum intensity of sound is heard, it corresponds to amplitude of the wave. For the first harmonic the length of the organ pipe equals one-fourth the wavelength of the wave. Hence,

Where, l is the length of the pipe and λ is the wavelength

Now velocity of wave

where f is the frequency of the wave.

(b) We know that velocity of air is given by

where γ is the ratio of specific heat at constant pressure to specific heat at constant volume for air, R is the universal gas constant, T is temperature and M is the mass of the gas. Keeping everything constant except temperature,

Let the velocity of sound in air at 0° C be v_{0} and the velocity at temperature 20° be v_{20}, then

(c) When water is replaced with mercury all the observations will remain same, however mercury is more reflective than water and therefore the intensity of the sound heard will be increased.

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