Question

A sound wave has a frequency of 695 Hz in air
and a wavelength of 0.49 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

This question involves the concepts of the speed of sound, frequency, and temperature.

The temperature of the air is "14.24 °C".

Temperature of Air

First, we find the speed of sound at the given temperature:

v = fλ

where,

• v = speed of sound = ?
• f = frequency = 695 Hz
• λ = wavelength = 0.49 m

Therefore,

v = (695 Hz)(0.49 m)

v = 340.55 m/s

Now, the relationship between the speed of sound and temperature can be given by the following formula:

$\frac{v}{v_o} = \sqrt{\frac{T}{273\ k}}\\\\T = (273\ k)(\frac{v}{v_o})^2$

where,

• T = Temperature = ?
• v = speed of sound in air at given temperature = 340.55 m/s
• v₀ = speed of sound in air at 0°C = 332 m/s

Therefore,

$T = (273\ k)(\frac{340.55\ m/s}{332\ m/s})^2$

T = 287.24 k = (278.24 k -273) °C

T = 14.24 °C

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