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A person sitting at a distance of 10m fr...

A person sitting at a distance of `10m` from a point source of sound of power `W_(0)` writes down the following equation for the waves received by him.
`y=Asin(20pix+7000pit)`
`(a)` Determine the density of the air, if the Bulk modules of air `=1.40xx10^(5)Nm^(-2)`
`(b)` If the largest pressure amplitude tolerable to a human car is `28Pa` then determine the maximum power `W_(0)` of the second source and the displacement amplitude `A` of the waves receive by him.

Text Solution

Verified by Experts

Since, `y=Asin(2pix+7000pit)=Asin(kx+omegat)`
`:. K=20pi`, `omega=7000pi`
`:. ` Velocity of sound `v=omega//k=350m//s`
Given that `B=1.48xx10^(5)`
`:. V=sqrt((B)/(rho))`
`rho=B//v^(2)=(1.40xx10^(5))/((350)^(2))=1.143kg//m^(3)`
Pressure amplitude is defined as `P_(0)=BkA`
Given that max. `P_(0)=28Pascal`
`k=(20)pi`
`:. A=(P_(0))/(BK)=(28)/(20pixx1.40xx10^(5))=3.183mu m`
Intensity received by the person `I=W_(0)//(4pi(10)^(2))`
Also `I=(vP_(B)^(2))/(2B)`
`W_(0)=(4pi(10)^(2)vP_(0)^(2))/(2B)=(200pixx(350)(28)^(2))/(2xx(1.4xx10^(5)))=615.75 "Watts"`.
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