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Question
Answer briefly.
What is the effect of pressure on the velocity of sound?
Solution
- Let v be the velocity of sound in the air when the pressure is P and density is ρ.
- Using Laplace's formula, we can write,
v = `sqrt((gamma"P")/rho)` ....(1) - If V be the volume of gas having mass M then, `rho = "M"/"V"`
- Substituting ρ in equation (1), we get,
v = `sqrt((gamma"PV")/("M"))` ....(2) - But according to Boyle’s law,
PV = constant (at constant temperature)
Also, Also, M and γ are constant.
∴ v = constant - Hence, the velocity of sound does not depend upon the change in pressure, as long as the temperature remains constant.
- For a gaseous medium, PV= nRT. Substituting in equation (2), we get,
v = `sqrt((gamma"nRT")/("M"))` - Thus, even for a gaseous medium obeying the ideal gas equation, the velocity of sound does not depend upon the change in pressure, as long as the temperature remains constant.
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