Question

If a wavelength is much larger than the diameter of a loudspeaker, the speaker radiates in all directions, much like a point source. On the other hand, if the wavelength is much smaller than the diameter, the sound travels in an approximately straight line in front of the speaker. Find the frequency of a sound wave that has a wavelength ten times the diameter of a $30cm$ speaker. Take the speed of sound to be $340m{s}^{-1}$.

Answer 1

The wavelength of sound is ten times the diameter of a $30cm$ speaker.

$\lambda =10\times d_{speaker}=10\times 30=300cm=3m$

The speed $v,$ frequency $f$ and wavelength $\lambda$ are related as:

$v=f\times \lambda$

$\Rightarrow f=\frac{v}{\lambda }$

Given:

Speed $v=340m/s$

So

Frequency $f=\frac{340m/s}{3m}=113.33$ sec${}^{-1}$ $=113.33Hz$