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

Question

Two small stereo speakers A and B that are 1.40 m apart are sending out sound of wavelength 34.8 cm 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 1.50 m 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

given

wavelength of the sound, lamda = 34.8 cm = 0.348 m

A) for constructive intereference,

path difference = n*lamda (n = 0,1,2,3,4,5...)

1.5 - x = n*lamda

x = 1.5 - n*lamda

for n = 0,

x = 0

for n = 1,

x = 1.5 - 1*0.348 = 1.152 m

for n = 2,

x = 1.5 - 2*0.348 = 0.804 m

for n = 3,

x = 1.5 - 3*0.348 = 0.456 m

for n = 4,

x = 1.5 - 4*0.348 = 0.108 m

B)

for constructive intereference,

path difference = n*lamda/2 (n = 1,3,5,7...)

1.5 - x = n*lamda/2

x = 1.5 - n*lamda/2

for n = 0,

x = 0

for n = 1,

x = 1.5 - 1*0.348/2 = 1.326 m

for n = 3,

x = 1.5 - 3*0.348/2 = 0.978 m

for n = 5,

x = 1.5 - 5*0.348/2 = 0.63 m

for n = 7,

x = 1.5 - 7*0.348/2 = 0.282 m

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