You are standing 2.5 m directly in front of one of the two loudspeakers shown in the figure. They are 3.0 m apart and both are playing a 686 Hz tone in phase. As you begin to walk directly away from the speaker, at what distances from the speaker do you hear a minimum sound intensity? The room temperature is 20 degrees Celsius.
v=343 m/s at 20 degrees
destructive interference: l1-l2=(n+1/2)lambda where n=0, 1, 2...
The Attempt at a Solution
First I found the wavelength which is 0.5 m. Then I drew a right angle triangle, where the distance between the speakers is 3 m and the other side is 2.5 m. Then I determined the hypotenuse, which is 3.91 m. For destructive interference, the sounds from both speakers should be out of phase and this happens when the person is a distance of (n+1/2)lambda away from one speaker and a distance of lambda away from the other (I think). So then I took the value 3.91, and added lambda/2 to get 4.16 for the hypoteneuse and solved for the other side to get 2.9 m. I did this another two times by adding 3/2 lambda and then 5/2 lambda to 3.91 (since the question is asking for the third value...this isn't explicitly stated, but I tried entering my answer with only 1 or 2 distances but I got a message saying I need to enter more values. When I entered 3 of them, a message came up saying I should re-check my calculations). I was wondering if there is something wrong with my logic.