Waves

JEE Main level, single correct, medium

15 of 142

Question 15 of 142

Assume that the displacement (s) of air is proportional to the pressure difference (Δp)\left(\Delta p\right) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air(ρ)\left(\rho \right) and the frequency (f). If Δp 10Pa,n 300m/s,p 1kg/m3\Delta p~10Pa,n~300m/s,p~1kg/{m}^{3} f 1000Hzf~1000Hz, then s will be of the order of (take the multiplicative constant to be 1 )

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Answer: (A) 3100mm\dfrac{3}{100}mm

S=P0BKS=\dfrac{{P}_{0}}{BK}
=P0PV2ωV=\dfrac{{P}_{0}}{P{V}^{2}\dfrac{\omega }{V}}
=P0PVω=\dfrac{{P}_{0}}{P{V}_{\omega }}
=101×1000×300m=\dfrac{10}{1\times 1000\times 300}m
≃3100mm≃\dfrac{3}{100}mm

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