Answer:
[tex]-14.2^{\circ}C[/tex]
Explanation:
First of all, we can find the speed of the sound wave, which is given by:
[tex]v=f \lambda[/tex]
where
f = 645 Hz is the frequency
[tex]\lambda=0.5 m[/tex] is the wavelength
Substituting,
[tex]v=(645 Hz)(0.5 m)=322.5 m/s[/tex]
Now we can find the temperature of the air by using the following relationship:
[tex]v = 331 m/s + 0.6 T[/tex]
where T is the temperature in Celsius degrees. Since we know v = 322.5 m/s, we can re-arrange the formula to find the temperature:
[tex]T=\frac{v-331 m/s}{0.6}=\frac{322.5 m/s-331 m/s}{0.6}=-14.2^{\circ}C[/tex]
