In the diagram, sound with wavelength travels rightward from a source and throug
ID: 1965115 • Letter: I
Question
In the diagram, sound with wavelength travels rightward from a source and through a tube that consists of a straight portion and a half-circle. Part of the sound wave travels through the half-circle and then rejoins the rest of the wave, which goes directly through the straight portion. This rejoining results in interference. What is the smallest radius r that results in an intensity minimum at the detector? State your answer in terms of the given variables using vs for the speed of sound and if necessary.
Explanation / Answer
path difference=r-2r=(-2)r
for minimum intensity at the detector
phase diffrence=(2n+1)
phase diffrence=K( path diffrence)
(2n+1)=2/*(-2)r
(-2)r=/2 *(2n+1)
for minimum r, n=0
(-2)rmin=/2
rmin=/[2(-2)]=0.438