please show work .maybe how to get there?? i get double slits but this seems wie

Question

please show work .maybe how to get there?? i get double slits but this seems wierd

A 900 Hz sound wave is produced on the source side of the tube shown in the figure. The sound travels to the right along both the straight and the curved path to a detector. (a) What is the smallest value of r such that a minimum in sound intensity will be heard at the detector end? (b) What are the two smallest values of r such that a maximum in sound intensity will be heard at the detector

i was asked for more info but none was given.. a hint is that the wavelength is c/f

Explanation / Answer

In use formula

Path difference=pi*r-2r

Solve

=1.14r

a)For minimum, path difference=lamda/2

lamda=v/f

Put the value

=343/900=0.3811m

1.14r=0.3811/2

Solve

=0.167m

b)For maximum,

1.14r=n*lamda

For smallest 2 values,

Then n.. and r..

n=1,2

r=0.334m,0.668m

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