A sound wave of 40.0 cm wavelength enters the tube shown in the figure at the source end. What must be the smallest radius r of the curved path such that a maximum intensity will be heard at the detector end?

The smallest value of r is cm.

Answer

Sound travels through two
different paths,
through the curved tube L_{1 }and
through the straight tube L_{2} . The path length difference between the two sound
waves is

Since we want **maximum sound** at the detector, the relationship between the path length
difference and the wavelength is

But since we want a non-zero value of r, we take the smallest non-zero of DL.

2-4 Interference

Example 2