Question

You are standing2.5m directly in front of one of the two loudspeakers shown in the figure. They are 3.0m 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 roomtemperature is 20 .Express your answer numerically using two significant figures. If there is more than one answer, enter your answers in ascending order separated by commas.If you could please give me a clear answer and solution - thank you so very much.

Answer 1

speed of sound at 20 C= 343 m/s
wavelength= speed/freq.=343/686=.50 m

one of the waves would travell 2.5 m and the other would travell (6.25+9)^(0.5)=3.91
path diff. = 1.41m

since the tunes are in phase the path diff. should be some integer times wavelength.
1.41=n*.5
n=2.82~3 (approx.)
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when path diffrence would be 3.5 times the wavelengh destructive interference would occur
path diff.=3.5*.5=1.75
let the distance be x
(x^2 + 9)^(.5) - x =1.75
x^2+9=3.0625+x^2 +3.5x
x=1.70
similarly work out with path diffrences of "1.5,2.5,4.5, 5.5,6.5 ,7.5, 8.5 times wavelength" and so on

As the man moves away from the speaker the path diffrence decreases and when the man is at an infinite distance it is zero.
when the distance is zero the path diffrence is 3m

so the path diffrence can never be greater than 3m.
do not take path diffrence equal to "6.5,7.5,8.5 times wavelength" and so on.