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Chapter 2: Q34E (page 540)

Small speakers A and B are driven in phase at 725 Hz by the same audio oscillator. Both speakers start out 4.50 m from the listener, but speaker A is slowly moved away (Fig. E16.34). (a) At what distance d will the sound from the speakers first produce destructive interference at the listener鈥檚 location? (b) If A is moved even farther away than in part (a), at what distance d will the speakers next produce destructive interference at the listener鈥檚

Short Answer

Expert verified

The range is 0.518m,0.303m,0.086m,0.126m

Step by step solution

01

Concept of the destructive interference

The path difference is given as未谤=(n+12)位 where,r1is the path length of the first speaker andr2is the path length of the second speaker

02

Rearrangement of position of the minimums with respect to distance from first speaker

The path difference is given by

r2-r1=n+12位1.25-r2-r1=n+12位r1=121.25-n+12位

The wavelength of the sound wave is given as

位=vf=3448脳102=0.429m

03

STEP 3 Plug in wavelength into the r1 and find all minimums that give r1 = [0,1.25 m] because we look for points between the speakers only: 

Equation is given byr1=121.25-n+12位

For n=0

role="math" localid="1664341848808" r1=121.25-0+120.429=0.518m

For n = 1

r1=121.25-1+120.429=0.303m

For n = 2

r1=121.25-2+120.429=0.089m

For n = 3

r1=121.25-3+120.429=0.126m

Therefore, the range is 0.518m,0.303m,0.086m,0.126m

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Most popular questions from this chapter

Two loudspeakers, A and B (see Fig. E16.35), are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. The frequency of the sound waves produced by the loudspeakers is 206 Hz. Consider a point P between the speakers and along the line connecting them, a distance x to the right of A. Both speakers emit sound waves that travel directly from the speaker to point P. For what values of x will (a) destructive interference occur at P; (b) constructive interference occur at P? (c) Interference effects like those in parts (a) and (b) are almost never a factor in listening to home stereo equipment. Why not?

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