In a student laboratory exercise, the wavelength of a 68,300 Hz ultrasound wave is measured to be 0.507 cm. Find the air temperature (in K).

Answer 1

The relationship between the speed of a wave (v_w), its frequency (f), and wavelength (λ) is:

v_w = fλ = (68300)(0.507) cm/s = 34628.1 cm/s

Assuming sea-level, the speed of sound as a function of T is:

v_w = (331 m/s) (T / 273K)^1/2

∴ T = ( v_w / 33100 cm/s )² 273K

Substitute 34628.1 for v_w and solve for T = 298.8K