A metre-long tube open at one end, with movable piston at the other end, shows resonance with a fixed frequency source (a tuning fork of frequency 340 Hz) when the tube length is 25.5 cm or 79.3 cm. Estimate the speed of sound in air at the temperature of the experiment. The edge effects may be neglected.

Question

A metre-long tube open at one end, with movable piston at the other end, shows resonance with a fixed frequency source (a tuning fork of frequency 340 Hz) when the tube length is 25.5 cm or 79.3 cm. Estimate the speed of sound in air at the temperature of the experiment. The edge effects may be neglected.

Philoid · Accepted Answer

Given,

Frequency of the turning fork, f = 340 Hz

Length of pipe, l = 25.5 cm = 0.255 m

Since the given pipe is attached with a piston at one end, one of its end is closed. So, 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 by

l = π/4

∴ λ = 4l

⇒ λ = 4 × 0.255 m

⇒ λ = 1.02 m

The speed of the sound is given by

v = fλ

⇒ v = 340 Hz × 1.02 m

⇒ v = 346.8 m s^-1