Two small speakers $A$ and $B$ are driven in step at $725 \mathrm{~Hz}$ by the same audio oscillator. These speakers both start out $4.50 \mathrm{~m}$ from the listener, but speaker $A$ is slowly moved away. (See Figure $12.41 .)$ (a) At what distance $d$ will the sound from the speakers first produce destructive interference at the location of the listener? (b) If $A$ keeps moving. at what distance $d$ will the speakers next produce destructive interference at the listener? (c) After $A$ starts moving away, at what distance will the speakers first produce constructive interference at the listener?
Added by Katherine C.
Step 1
Given frequency, \( f = 725 \, \text{Hz} \) Speed of sound in air, \( v = 344 \, \text{m/s} \) We know that \( v = f \lambda \) Therefore, \( \lambda = \frac{v}{f} = \frac{344}{725} = 0.474 \, \text{m} \) Show more…
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Two identical loudspeakers are located at points $A$ and $B, 2.00 \mathrm{~m}$ apart. The loudspeakers are driven by the same amplifier and produce sound waves with a frequency of $784 \mathrm{~Hz}$ Take the speed of sound in air to be $344 \mathrm{~m} / \mathrm{s}$. A small microphone is moved out from point $B$ along a line perpendicular to the line connecting $A$ and $B$ (line $B C$ in Fig. $P 16.65$ ) (a) At what distances from $B$ will there be destructive interference? (b) At what distances from $B$ will there be constructive interference? (c) If the frequency is made low enough, there will be no positions along the line $B C$ at which destructive interference occurs. How low must the frequency be for this to be the case?
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