Two speakers are driven by the same amplifier and emit sinusoidal waves in phase

Question

Two speakers are driven by the same amplifier and emit sinusoidal waves in phase. The speakers are on the x axis a distance d= 2.50 m apart. The frequency of the sound waves produced by the loudspeakers is 200 Hz. For a point on the x axis between the two speakers, at what values of x will (a) destructive interference occur, and b) constructive interference occur? (c) Can destructive or constructive interference occur at a point on the x axis to the right of both speakers or to the left of both speakers? Explain. [Assume the temperature is 86 degree F (30 degree C).]

Explanation / Answer

speed of the sound is

V = 331.3+ 0.6 T) = 331+0.6(30) = 349.3 m/s

Constructive interference will occur when the difference in the distances traveled by

the two sound waves in reaching point P is an integer number of wavelengths. That

is, when

lamada = v/f= 349.3/200 Hz = 1.745 m

(d-x)- x = n lmada

x= d- n lamda/2

for n = 0

x= d/2 = 2.5/2 = 1.25 m

for n= 1

x= d- n lamda/2

=2.5-1(1.745)/2

=0.376 m

for distrutive interference

(d-x)- x = n lmada/2

d- n lamda/2 = 2x

x= d- n lamda/4

x= d/4 = 2.5/4 = 0.625 m

for n = 1

x= d- n lamda/4

=2.5-1(1.745)/4

=0.188 m

(c)

Yes, all. All of them between both speakers.

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