Find the air temperature (in K).

Question

In a student laboratory exercise, the wavelength of a 52,300 Hz ultrasound wave is measured to be 0.660 cm. Find the air temperature (in K).

Answer 1

In a student laboratory exercise, the wavelength of a 52,300 Hz ultrasound wave is measured to be 0.660 cm. Find the air temperature (in K).

Frequency = 52300 Hz

Wave Length = 0.66* 10^-2 m

Velocity = Frequency * Wavelength

52300*0.66 *10^-2 m/s

= 345.18 m/s

V₀ / V_T = Sqrt ( 273/ T ) , V₀ = Speed of sound at 273 K = 332m/s , Vt = Speed of sound at T K

332/345.18 = Sqrt ( 273/T)

T / 273 =( 345.18 * 345.18)/( 332*332)

T = 273*345.18*345.18/(332*332)

=295K ( approx)