Answer:
[tex]-58.3^{\circ}C[/tex]
Explanation:
The relationship between frequency, wavelength and speed of a wave is
[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:
f = 634 Hz
[tex]\lambda=0.47 m[/tex]
So its speed is
[tex]v=(634)(0.47)=298 m/s[/tex]
The speed of sound in dry air depends on the temperature according to the equation
[tex]v=333 + 0.6T[/tex]
where
T is the temperature
In this problem,
v = 298 m/s
Therefore, solving the equation for T, we find the temperature of the air:
[tex]T=\frac{v-333}{0.6}=\frac{298-333}{0.6}=-58.3^{\circ}C[/tex]
