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Chapter 11: Problem 42

A sound wave with intensity \(25 \mathrm{mW} / \mathrm{m}^{2}\) interferes destructively with a sound wave that has an intensity of $28 \mathrm{mW} / \mathrm{m}^{2} .$ What is the intensity of the superposition of the two?

Short Answer

Expert verified
Answer: The intensity of the superposition of the two sound waves is 3 mW/m².

Step by step solution

01

Identify the given intensities

We are given the intensities of two sound waves: Intensity 1: \(I_1 = 25 \mathrm{mW} / \mathrm{m}^{2}\) Intensity 2: \(I_2 = 28 \mathrm{mW} / \mathrm{m}^{2}\)
02

Use the principle of superposition for destructive interference

The principle of superposition states that when two waves interfere destructively, we should subtract the individual intensities to obtain the final intensity. So, we will calculate the resulting intensity using this formula: \(I_r = |I_1 - I_2|\)
03

Calculate the final intensity

Now, we will plug the values of the intensities into the formula and calculate the final intensity of the superimposed sound waves: \(I_r = |25\mathrm{mW}/\mathrm{m}^2 - 28 \mathrm{mW}/\mathrm{m}^2|\) \(I_r = |(-3) \mathrm{mW}/\mathrm{m}^2|\) \(I_r = 3 \mathrm{mW}/\mathrm{m}^2\) The intensity of the superposition of the two sound waves is \(3\mathrm{mW}/\mathrm{m}^2\).

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Most popular questions from this chapter

Two speakers spaced a distance \(1.5 \mathrm{m}\) apart emit coherent sound waves at a frequency of \(680 \mathrm{Hz}\) in all directions. The waves start out in phase with each other. A listener walks in a circle of radius greater than one meter centered on the midpoint of the two speakers. At how many points does the listener observe destructive interference? The listener and the speakers are all in the same horizontal plane and the speed of sound is \(340 \mathrm{m} / \mathrm{s} .\) [Hint: Start with a diagram; then determine the maximum path difference between the two waves at points on the circle. I Experiments like this must be done in a special room so that reflections are negligible.
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