In a student laboratory exercise, the wavelength of a 44,300 Hz ultrasound wave is measured to be 0.788 cm. Find the air temperature (in K).

Answer 1

The wave speed v = fλ when f = 44,300 s^-1 and λ = 7.88 mm is v = (4.43 x 10⁴ s^-1) (7.88 x 10^-3 m) = 349 m/s. The common expression for sound speed in air is v ≅ 331.3 + 0.606 °C for temperature in Celsius, but this approximation is almost one degree off in this case. So use the exact expression instead, v = 20.05 √T, then √T = 349 / 20.05 and T = 303 K.