A 50cm long hollow glass cylinder is open at both ends and is suspended in air.

Question

A 50cm long hollow glass cylinder is open at both ends and is suspended in air. A source of sound that produces a pure frequency is placed close to one end of the tube. The frequency of the sound source is slowly increased from a very low value. The tube is first observed to resonate when the source frequency is 320Hz.

- Calculate the speed of the sound in the tube.

- The frequency of the source is slowly increased until resonance occurs again FOR THE THIRD TIME. Calculate the frequency at which this happens.

- Calculate the frequency when resonance occurs for the FIFTH time.

- The end of the cylinder opposite the end where the sound source is positioned is tightly sealed with a rigid metal plate. Calculate the first THREE resonant frequencies(lowest to highest).

- If the apparatus is now placed in helium gas instead of air, do the resonant frequencies referred to in previous parts of this question increase or decrease? Give your reasoning.

- The original air-filled apparatus now suffers a temp decrease of 40 celcius, do the resonant frequencies referred to in previous parts of this question increase or decrease? Give your reasoning.

Explanation / Answer

for open pipe  at both ends, we ahve

fn = nv/2L

then the speed is,

(320) = (1)(v)/(2)(0.5)

v = 320 m/s

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for the third time, we have

f3 = (3)(320)/(2)(0.5) = 960 Hz

for the fift time, we have

f5 = (5)(320)/(2)(0.5) = 1600 Hz

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