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.

Sound travels through two different paths, through the curved tube L₁ and through the straight tube L₂ . 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.