Question

Ina resonance tube experiment to determine the speed of the sound in air, a pipe of diameter 5 cm is used. The column in pipe resonates with a tuning fork of frequency 480 Hz when the minimum length of the air column is 16 cm. Find the speed of sound (in m/s) in air column at room temperature.

Answer 1

Given- $f=480Hz,d=5cm$ , or $r=5/2=2.5cm=0.025m$ ,

minimum length of air column i.e. $l_1=16cm=0.16m$ ,

the end correction of the tube will be , $e=0.6r$ ,

but , $e=(l_2-3l_1)/2$ ,

or $0.6\times 0.025=(l_2-0.16)/2$ ,

or $l_2=0.51m$ ,

therefore speed of sound in air column ,

$v=2f(l_2-l_1)$ ,

or $v=2\times 480(0.51-0.16)=336m/s$