In a student laboratory exercise, the wavelength of a 48,300 Hz ultrasound wave is measured to be 0.716 cm. Find the air temperature (in K).

Question

In a student laboratory exercise, the wavelength of a 48,300 Hz ultrasound wave is measured to be 0.716 cm. Find the air temperature (in K).

Answer 1

Let's establish some quick facts:

1. speed of sound is affected by temperature, the frequency is not affected
2. the equation for this is: speed of sound = (331m/s) √T/273K
3. Speed of Sound = wavelength * frequency

Final Equation and Answer:

0.716cm * 48,300Hz = (331m/s) √T/273K

34,582.8cm/s = 331m/s√T/273K

(345.828m/s)/331m/s = (331m/s√T/273K)/331m/s

(1.0448m/s)² = (√T/273K)²

(1.092m/s)273K = (T/273K)273K

298.007K