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Two speakers are wired to emit identical sounds in unison. The wavelength in air of the sounds is...

Question:

Two speakers are wired to emit identical sounds in unison. The wavelength in air of the sounds is 6 m. Do the sounds interfere constructively or destructively at a point 10 m from both speakers?

1. Destructively

2. Neither

3. Constructively

Constructive Interference

The two wave meet as a point they interfere with each other. The amplitude of the resultant wave will be maximum when the interference is constructive. The interference will be constructive if the phase difference between the two waves is integral multiple of {eq}2 \pi {/eq} or the path difference between the two waves is integral multiple of the wavelength of the wave.

Answer and Explanation:


Given :

  • The distance traveled by the wave from first speaker to the required point is, {eq}l_1 = 10 \ m {/eq}
  • The distance traveled by the wave from second speaker to the required point is, {eq}l_2 = 10 \ m {/eq}


The path difference between the sound reaching the required point from both the speakers is,

{eq}\begin{align*} \Delta p &= l_2 - l_1 \\ \Delta p &= 10-10 \\ \Delta p &= 0 \end{align*} {/eq}

As the path difference is zero, so the interference will be constructive

That makes option (3) correct.


Learn more about this topic:

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Constructive and Destructive Interference

from CLEP Natural Sciences: Study Guide & Test Prep

Chapter 8 / Lesson 16
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