Waves and Sound (Module 7)

1. In the upper atmosphere at altitudes where commercial airlines travel, we find extremely cold temperatures. What is the speed of sound (in metric units) for a temperature of -57.8 degree F? Note that the temperature is in degree F.
2. What frequency of sound traveling in air at 26 degree C has a wavelength of 4.2 m?
3. A 331 Hz sound wave travels through a gas. If the wavelength of the sound is 1.2m, what is the speed of sound in the gas?

1.
The conversion between Fahrenheit degree (F) and Celsius degree (C) is
$C = 5/9(F-32) =5/9(-57.8-32) =-49.89$ Celsius degree
The speed of sound in air is given by
$V = 331.3 +0.606*t (m/s)$ where $t$ is the temperature in Celsius degree
$V = 331.3+0.606*(-49.89) =301.067 m/s$
2.
The speed of sound in air V, at a temperature t (in Celsius degree) is given by
$V = 331.3 +0.606*t =331.3+0.606*26 =347.056 m/s$
Let F be the frequency of the sound , V its speed and L its wavelength. Then by DEFINITION
$L = V/F$
Hence $F = V/L =347.056/4.2 =82.63 Hz$
3.
Let V be the speed of sound, L its wavelength and F its frequency. By DEFINITION
$L= V/F$
Hence $V =F*L = 331*1.2 =397.2 m/s = 397.2 m/s$