Question

A tuning fork vibrating with a frequency of 512 Hz is kept close to the open end of a tube filled with water (Fig.). The water level in the tube is gradually lowered. When the water level is 17 cm below the open end, maximum intensity of sound is heard. If the room temperature is 20ºC, calculate

(a) Speed of sound in air at room temperature

(b) Speed of sound in air at 0ºC

(c) If the water in the tube is replaced with mercury, will there be any difference in your observations?

Answer 1

Let us consider the following diagram

For maximum intensity –

(a) L = \(\frac{\lambda}{4}\)

Or λ = 4L

v = vλ = v × 4L

= 512 × 4 × 17 × 10^-2 

= 348.16 m/s

(b) As, v ∝\(\sqrt T\)  (T = Temperature)

\(\frac{v_{20}}{v_0}=\sqrt {\frac{273+20}{273+0}}\)

\(\frac{v_{20}}{v_0}\) = 1.04

Or v₀ =\(\frac{v_0}{1.04}=\frac{348.16}{1.04}\) = 334.8 m/s

(c) Water and mercury in tube reflects the sound into air column to form stationary wave and reflection is more in mercury than water as mercury is more denser than water. So, intensity of sound heard will be longer but reading does not change as medium in tube (air) and running fork are same.