Answer:
[tex]-58.3^{\circ}C[/tex]
Explanation:
The frequency and the wavelength of a wave are related by the equation
[tex]v=f\lambda[/tex]
where
v is the speed
f is the frequency
[tex]\lambda[/tex] is the wavelength
For the sound wave in this problem, we have
f = 634 Hz (frequency)
[tex]\lambda=0.47 m[/tex] (wavelength)
Therefore, the speed of the wave is
[tex]v=(634)(0.47)=298 m/s[/tex]
The speed of sound in air depends on the temperature according to the equation
[tex]v=333+0.6 T[/tex]
where T is the temperature.
In this problem, we know the speed, so we can calculate the temperature:
[tex]T=\frac{v-333}{0.6}=\frac{298-333}{0.6}=-58.3^{\circ}C[/tex]
