- [2081 B/C] Calculate the wavelength of wave in air at 25oC if the frequency of sound wave is 256 Hz and velocity of sound at 0oC is 330 [latex]ms^{-1}[/latex]. [2] Ans: 1.35 m
Solution:
Given,
Wavelength at 25oC ([latex]\lambda_{25}[/latex]) =?
Frequency (f) = 256 Hz
Temperature (T25) = 25oC = 25 + 273 = 298 K
Temperature (To) = 0oC = 0 + 273 = 273 K
Velocity at 0oC ([latex]v_o[/latex]) = 330 m/s
We know that,
[latex]v \propto \sqrt{T}[/latex]
Or, [latex]\frac{v_{25}}{v_o} = \sqrt{\frac{T_{25}}{T_o}}[/latex]
Or, [latex]\frac{f\times \lambda_{25}}{v_o} = \sqrt{\frac{298}{273}}[/latex]
Or, [latex]\frac{256\times \lambda_{25}}{330} = 1.045[/latex]
Or, [latex]\lambda_{25} = \frac{330\times 1.045}{256}[/latex]
= 1.35 m/s
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