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The pressure wave, p = 0.01 sin (1000t -...

The pressure wave, `p = 0.01 sin (1000t - 4x] Nm^(-2)` corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is T. the speed of sound produced by the same blade and at same frequency is found to be 340 `ms^(-1)`. Find out and calculate the value of `(T)/(10)` upto two decimal places.

Text Solution

Verified by Experts

The correct Answer is:
`23.22`
`P=0.01 sin [1000t -4x] , T=0^(@)C =273.15`
`rArr k=4`
`rArr (2pi)/(lambda)=4`
`rArr lambda =(pi)/(2)`
`omega =1000`
`rArr v=(1000)/(2pi)`
`v_(1) =v lambda`
`=(1000)/(2pi) xx (pi)/(2)`
`:.v_(1)=250 m//s`
Alternate Method for `v_(1)`:
`v_(1)=(omega)/(k)`
`=(1000)/(4)`
`:.v_(1) =250 m//s`
`v_(2) =340 ms^(-1)`
`rArr (v_(1))/(v_(2))= sqrt((T_(1))/(T_(2)))`
`rArr (v_(1)^(2))/(v_(2)^(2)) =(T_(1))/(T_(2))`
`rArr T_(2) = (v_(2)^(2))/(v_(1)^(2)) xx T_(1) =((340)/(250))^(2) xx (273.15)`
`=1.85 xx 273.15`
`=505.33K`
`:.T_(2) = 232.18^(@)C`
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