Answer to Question #161500 in Optics for Salman

Question

Why does a clarinet play a lower note than a flute when both instrument are about the same length?

Answer 1

The flute is an open-end pipe for the air, while the clarinet is closed-end pipe. The flute is about 0.6 meters long and on the fundamental frequency it can produce the wavelength that is twice as long as the pipe, so let's calculate the wavelength:

$$\lambda=2L=2\cdot0.6\ m=1.2\ m.$$

Then, we can calculate the frequency of the note:

$$f=\dfrac{v}{\lambda}=\dfrac{340\ \dfrac{m}{s}}{1.2\ m}=283\ Hz.$$

The clarinet on the fundamental frequency can produce the wavelength that is four times as long as the pipe:

$$\lambda=4L=4\cdot0.6\ m=2.4\ m.$$

Then, we can calculate the frequency of the note:

$$f=\dfrac{v}{\lambda}=\dfrac{340\ \dfrac{m}{s}}{2.4\ m}=142\ Hz.$$

Therefore, as we can see from the calculations, the clarinet plays a lower note than the flute when both instrument are about the same length.