A student performed the experiment to measure the speed of sound in air using the resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and

Question

A student performed the experiment to measure the speed of sound in air using the resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance. Then, [2009]

Smart Achievers · Accepted Answer

(1, 4)

The length of the air column at the first resonance is somewhat shorter than $\frac{1}{4}$ th of the wavelength of the sound in air due to end correction (e).

$ℓ + e = \frac{λ}{4}$ $\Rightarrow ℓ = \frac{λ}{4} - e$

Hence, at second resonance the length of the air column is more as compared to first resonance. Now, longer the length of air column, more is the absorption of energy and lesser is the intensity of sound heard.

Solution

1 the intensity of the sound heard at the first resonance was more than that at the second resonance

2 the prongs of the tuning fork were kept in a horizontal plane above the resonance tube

3 the amplitude of vibration of the ends of the prongs is typically around 1 cm

4 the length of the air-column at the first resonance was somewhat shorter than 1/4 of the wavelength of the sound in air.

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