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?
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
$V = 331.3+0.606*(-49.89) =301.067 m/s$
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 $F = V/L =347.056/4.2 =82.63 Hz$
Let V be the speed of sound, L its wavelength and F its frequency. By DEFINITION
Hence $V =F*L = 331*1.2 =397.2 m/s = 397.2 m/s$