Question

A sound wave has a frequency of 745 Hz in air and a wavelength of 0.55 m. What is the temperature of the air? Relate the speed of sound in air to temperature in units of Kelvin, but answer in units of Celsius. Assume the velocity of sound at 0 ◦C is 332 m/s. Answer in units of degC

Answer 1

The temperature of the air at the given speed of sound wave is 142.8 ⁰C.

Temperature of air

The temperature of the air at the given speed of sound and frequency is calculated as follows;

$v = 332\sqrt{1 + \frac{T}{273} }$

Velocity of the sound wave

v = fλ

v = 745 x 0.55

v = 409.75 m/s

Now, solve for the temperature;

$409.75 = 332 \sqrt{1 + \frac{T}{273} } \\\\1.234 = \sqrt{1 + \frac{T}{273} }\\\\1.234^2 = 1 + \frac{T}{273}\\\\0.523 = \frac{T}{273} \\\\T = 142.8 \ ^0C$

Thus, the temperature of the air at the given speed of sound wave is 142.8 ⁰C.

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