Numerical Solutions: Mechanical Waves

[2081 B/C] Calculate the wavelength of wave in air at 25^oC if the frequency of sound wave is 256 Hz and velocity of sound at 0^oC is 330 [latex]ms^{-1}[/latex]. [2] Ans: 1.35 m
Solution:
Given,
Wavelength at 25^oC ([latex]\lambda_{25}[/latex]) =?
Frequency (f) = 256 Hz
Temperature (T₂₅) = 25^oC = 25 + 273 = 298 K
Temperature (T_o) = 0^oC = 0 + 273 = 273 K
Velocity at 0^oC ([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