Two small stereo speakers A and B that are 1.40m apart are sending out sound of

Question

Two small stereo speakers A and B that are 1.40m apart are sending out sound of wavelength 33.5cm in all directions and all in phase. A person at point P starts out equidistant from both speakers and walks (see the figure (Figure 1) ) so that he is always 1.50m from speaker B. Limit your solutions to the cases where x?1.50m.

Part A

For what values of x will the sound this person hears be maximally reinforced?

Enter you answers in decreasing order separating them with commas.

Part B

For what values of x will the sound this person hears be cancelled?

Enter you answers in decreasing order separating them with commas

Explanation / Answer

Here , wavelength = 33.5 cm

A)

Now, for maximum hearing ,

path difference = n*wavelength

|x - 1.5| = n*0.335

as x is smaller than 1.5

x = 1.5 - n*0.335

now , x = 1.165 , 0.83 , 0.495 , 0.16 m

B)

for calcelling the hearing

path difference = ((2n+1)/2) *wavelength

|x - 1.5| = ((2n+1)/2)*0.335

x = 1.5 - ((2n+1)/2)*0.335

x = 1.3325 m , 0.9975 m , 0.6625 m,0.3275 m

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