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ICSE Class 9 Answered

Why and how mathematically is the speed of sound not dependent on pressure?
Asked by Rupa | 05 Jun, 2017, 02:12: PM
answered-by-expert Expert Answer
The doubt arises because the expression of the speed of sound has pressure in it. So, we appreciate the intellect behind this question. It is a genuine doubt and is ignored on the pretext of being trivial. Let us go through the explanation step by step.
 
1) The expression for the speed of sound in a gas is begin mathsize 12px style straight v equals square root of γP over straight rho end root end style. So, speed is dependent on pressure, density and γ.
2) Now, speed is dependent on density. This dependency arises when a change in the quantity causes a change in the desired variable. So, when density changes speed also changes.
 
3) Consider pressure. When pressure changes, the volume also changes. Here, the mass remains the same. So, the change in volume causes a change in density. So, effectively change in pressure and an equal change in density nullifies the effect and the speed remains unaffected due to change in pressure. Your doubt is genuine because pressure appears in the expression. But, one thing to note is that dependency occurs only when there is a change in the variable.
 
Answered by Romal Bhansali | 05 Jun, 2017, 03:58: PM
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