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A tuning fork of frequency 220Hz produce...

A tuning fork of frequency 220Hz produces sound waves of wavelength 1.5m in air at NTP. Calculate the increase in wavelength, when temperature of air in `27^(@)C`.

Text Solution

Verified by Experts

The correct Answer is:
`0.07`
Here v = 220 Hz, `T_0` = 273K ,
T = 273 + 27= 300K, `lamda = 1.5m`
Speed of sound at S.T.P. is
`v_0 = v lamda_0 = 220xx1.5 = 330 ms^(-1)`
`v/v_0=sqrt((T)/T_0)=sqrt(300/273)`
`:. v =sqrt((300)/(273))v_0=sqrt((300)/(273))xx330 ms^(-1)`
But `v = vlamda = 220 xx lamda`
`:. 220 xx lamda =sqrt(300/273)xx330`
or `lamda =lamda =sqrt(300/273)xx(330)/220=15.7 m`
Increase in wavelength `= lamda- lamda_0 = 1.57 -1.5 =0.07 m`
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