Question

A speaker generates a continuous tone of 440 Hz. In the drawing, sound travels into a tube that splits into two segments, one longer than the other. The sound waves recombine before being detected by a microphone. The speed of sound in air is 339 m/s. What is the minimum difference in the lengths of the two paths for sound travel if the waves arrive in phase at the microphone?

Answer 1

Answer:

The minimum difference between the lengths of the two tubes should be 0.385 meters.

Explanation:

As we known that for any two waves to arrive in phase at any point the difference in the path traveled by the waves should be an integral multiple of the wavelength of the wave.

Mathematically we can write:

$\Delta x=n\frac{\lambda }{2}$

For the given wave we have

$\lambda =\frac{v}{\nu }$

Applying values we get

$\lambda =\frac{339}{440 }=0.77m$

Thus the minimum difference in the lengths of the tubes can be obtained by putting the value of n = 1

$\therefore \Delta x=1\times \frac{0.77}{2}=0.385m$