Thu March 05, 2015 By: Pragyanshree Mishra

A meter long tube open at one end with a movable piston at the other end shows ressonance with  a fixed frequency source ( a tuning fork of frequency 340Hz) when the tube length is 25.5cm or 79.3 cm. estimate the speed of sound in air at the temperature of the expperiment. the edge  effect may be neglectd.

Expert Reply
Faiza Lambe
Thu March 05, 2015

Frequency of the turning fork, ν = 340 Hz.

As the given pipe is attached with a piston at one end, it will behave as a pipe with one end closed and the other end open.

Such a system produces odd harmonics.

The fundamental note in a closed pipe is given:

 begin mathsize 14px style straight l subscript 1 equals straight lambda over 4 end style

Length of the pipe, l1=25.5 cm = 0.255 m

begin mathsize 14px style therefore straight lambda equals 4 space straight l subscript 1 equals 4 cross times 0.255 equals 1.02 space straight m end style

The speed of sound is given by the relation:
begin mathsize 14px style straight nu equals straight nu space straight lambda equals 340 cross times 1.02 equals 346.8 space straight m divided by straight s end style
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