Physics - Sound Wave Question with Solution | TestHub

The speed of sound in an ideal gas is given by $v=\sqrt{\frac{\gamma RT}{M}}$, which implies $v\propto \sqrt{T}$, where $T$ is the absolute temperature.

The absolute temperatures are $T_{20}=20+273=293\text{ K}$ and $T_{40}=40+273=313\text{ K}$.

Since the frequency $f$ remains constant and $v=f\lambda$, the wavelength $\lambda$ is directly proportional to the speed of sound $v$.

Therefore, $\lambda \propto \sqrt{T}$.

The ratio of the wavelengths is $\frac{{\lambda }_{40}}{{\lambda }_{20}}=\sqrt{\frac{T_{40}}{T_{20}}}=\sqrt{\frac{313}{293}}$.

Answer: $\sqrt{\frac{313}{293}}$