Assume that the displacement (s) of air is proportional to the pressure difference ΔP created by a sound wave. Displacement (S) further depends on the speed of sound v, density of air ρ and the frequency f.If ΔP~$$10Pa$$, v~$$300m/s$$,ρ~$$1kg/m3$$ and f~$$1000Hz$$ then s will be of the order of $$($$ take multiplicative constant to be $$1)$$

Question

Assume that the displacement (s) of air is proportional to the pressure difference ΔP created by a sound wave. Displacement (S) further depends on the speed of sound v, density of air ρ and the frequency  f.If ΔP~$$10Pa$$, v~$$300m/s$$,ρ~$$1kg/m3$$ and f~$$1000Hz$$ then s will be of  the order of $$($$ take multiplicative constant to be $$1)$$

Infinity Learn · Accepted Answer

ΔP $$=$$ BK $$S0$$ , $$B=Bulk$$ modulus $$=$$ ρ$$V2$$​⇒ΔP $$=$$ ρ$$V22$$$$π$$f $$S0V$$    ∵$$K=$$ω$$V=2$$$$π$$fV]⇒$$S0$$ $$=$$ΔPρ$$V2$$$$π$$fTake multiplicative constant "$$2$$π" as $$1$$⇒$$S0$$ $$=101$$×$$300$$×$$1000=130mm$$

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