Solution

Given,

Frequency at 20° C (f₂₀) = 550 Hz
Wave length at 20°C (λ₂₀) = 60 cm = 0.6 m
Wave length at 0°C = ?

We have,

Velocity (v₂₀) = (f₂₀) x (λ₂₀) = 550 x 0.6 = 330 m/s

Again,

\(\frac{v_0}{v_{20}}=\sqrt{\frac{T_0}{{\displaystyle T}_{20}}}\)
Or, \(v_0=v_{20}\times\sqrt{\frac{T_0}{{\displaystyle T}_{20}}}\)
Or, \(v_0=330\times\sqrt{\frac{273}{\displaystyle293}}\)
∴ v₀ = 318.54 m/sec

Now,

\(\lambda_0=\frac{v_0}{f_{20}}=\frac{318.54}{550}=0.58m\)

Hence the wavelength at 0° C is 0.58 m