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 sound in air is V = 331.4 + (0.6*T) = 331.4+(0.6*30) = 349.4 m/sec

wavelength lamda = v/f = 349.4/200 = 1.75 m

a) For destructive interference

d2-d1 = (m+0.5)*lamda

x = (m+0.5)*lamda

For m = 0

x = lamda/2 = 1.75/2 = 0.875 m

x = 3*lamda/2 = 3*0.875 = 2.625 m

x= 5*lamda/2 = 5*0.875 = 4.375 m

and so on

b)For constructive interference

x = (m*lamda)

x = 0,1.75,(2*1.75),(3*1.75),(4*1.75),........

x = 0 ,1.75,3.5,5.25,7.......

c) at 2.625 m,destructive interference takes place

at 3.5 m, Construtive interference takes place

so right of both speakers or to the left of both speakers,destructive interference takes place

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