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If n is an odd integer, there will be destructive interference.Thanx man but u should knw that i also did it till this part couldn't do the rest of it
If n is an even integer, there will be constructive interference.
(It's the destructive interference that is being asked for in the question).
Using Pythagoras Theorem (right-angled triangles, etc.),
we can calculate that the difference in the distance from the most distant sound source to the microphone to that of the nearest sound source is 0.28 meter.
So, n.(lambda/2) = the path difference = 0.28 (meters) . . . . [1]
for constructive or destructive interference (depending on whether n is odd or even).
Now since speed of sound in air, v = f x lambda
we get: lambda = speed / frequency,
Now we know v; it is 330 m/s.
From [1] above, we can now say:
n.(330/2f) = the path difference = 0.28.
This can easily be re-arranged to give:
330n = 0.56f, which simplifies to:
f = 589n . . . . . .[2]
We know that if n = an even number, there will be constructive interference
but the question is asking for minima which is destructive
We know that if n = an odd number, there will be destructive interference.
If you put successive odd numbers into [2], you get the following frequencies:
n = 1; f = 589
n = 3; f = 1767
n = 5; f = 2945
n = 7; f = 4123
the frequency range in the question is 1000hz to 4000hz
Looking at the destructive interference table above, we can see that there are TWO frequencies that lie in this range
SO TWO MINIMA