A 1 metre long tube open at one end, with a movable piston at 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 793 cm. Estimate the speed of sound in air at the temperature of the experiment. The edge effects may be neglected.
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The speed of sound in the air is 346.8 m/s
Explanation:
As there is a piston at one end of the tube, it behaves as a closed organ pipe, which produces odd harmonics only.
Therefore, the pipe is in resonance with the fundamental note and the third harmonic (79.3 cm is about 3 times 25.5 cm ).
In the fundamental mode, λ/4 = l1 = 25.5
λ = 4 × 25.5 = 10^2 cm = 1.02 m
Speed of sound in air, υ =vλ = 340 × 1.02
= 346.8 m/s
Hence the speed of sound in the air is 346.8 m/s
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If the velocity of sound in air is 340 m/s calculate the (a) wavelength when frequency is 256 hertz (b) frequency and wavelength is 0.85 M ?
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