Question

. Calculate the wavelengths of sounds at the extremes of the audible range, 20 and 20, KHz, in 

30.0°C air.

Answer 1

Let's first find the speed of the sound in the air:

$$v=(331.3+0.606\cdot T)=(331.3+0.606\cdot30^{\circ}C)=349.5\ \dfrac{m}{s}.$$

Then, we can calculate the wavelengths of sounds (20 Hz and 20 kHz) from the wave-speed formula:

$$v=f\lambda,$$ $$\lambda_1=\dfrac{v}{f_1}=\dfrac{349.5\ \dfrac{m}{s}}{20\ Hz}=17.5\ m,$$ $$\lambda_2=\dfrac{v}{f_2}=\dfrac{349.5\ \dfrac{m}{s}}{20\cdot10^3\ Hz}=0.0175\ m.$$