Solution

Given,

Frequency of sound (f₂₀) = 512 Hz at 20°C
Wavelength of sound (λ₂₀) = 64.5 cm = 0.645 m at 20°C
Velocity of sound at 0°C (v₀) = ?

We have, the velocity of sound at 20°C is,

v₂₀ = f₂₀ x λ₂₀ = 512 x 0.645 = 330.24 m/s

Again,

\(\frac{v_0}{v_{20}}=\sqrt{\frac{T_0}{T_{20}}}\)
Or, \(v_0=v_{20}\times\sqrt{\frac{T_0}{T_{20}}}=330.24\times\sqrt{\frac{273}{293}}=318.77) m/s

Hence, the velocity of sound is 318.77 m/s