Answer to Question #164210 in Optics for Simen

Question

A source of sound frequency 550Hz emits waves of wavelength 600 mm in air at 20°C. What is the

velocity of sound in air at this temperature? What will be the wavelength of the sound from this source in air at 0°C?

Answer 1

Given quantities:

$\lambda = 600mm =0.6m \space\space\space\space frequency \space\space f = 550Hz$

velocity of sound $v = f\lambda = 0.6*550 = 330 m/s$

We know, $v \backsim \sqrt{T}$

here, $T_1 = t_1 + 273 = 20+273 = 293K$

$T_2 = t_2 + 272 = 0+273 = 273K$

$\to \large\frac{vv_1}{v_2} = \sqrt{\frac{T_1}{T_2}} \to v_2 = v_1*\sqrt{\frac{T_2}{T_1}} =$ $330*\large\frac{273}{293} =$ $318.5m/s$

$\lambda_2 = \large\frac{v_2}{f} = \frac{318.5}{550}$ $= 0.579m\to 579mm$