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Chapter 15: Problem 5

The speed of light waves in air is greater than the speed of sound in air by about a factor of a million. Given a sound wave and a light wave of the same wavelength, both traveling through air, which statement about their frequencies is true? a) The frequency of the sound wave will be about a million times greater than that of the light wave. b) The frequency of the sound wave will be about a thousand times greater than that of the light wave. c) The frequency of the light wave will be about a thousand times greater than that of the sound wave. d) The frequency of the light wave will be about a million times greater than that of the sound wave. e) There is insufficient information to determine the relationship between the two frequencies.

Short Answer

Expert verified
a) The frequency of the light wave will be about the same as that of the sound wave. b) The frequency of the light wave will be about a hundred times greater than that of the sound wave. c) The frequency of the light wave will be about a thousand times greater than that of the sound wave. d) The frequency of the light wave will be about a million times greater than that of the sound wave. Answer: d) The frequency of the light wave will be about a million times greater than that of the sound wave.

Step by step solution

01

Recall the wave speed formula.

The wave speed formula relates the speed(v), frequency(f), and wavelength(λ) of a wave: v = fλ
02

Write the given information

We are given that the speed of light waves in air is greater than the speed of sound in air by a factor of a million, meaning: Speed of light (v_l) = 1,000,000 × Speed of sound (v_s) And, we are also given that both light and sound waves have the same wavelength: λ_l = λ_s
03

Use the wave speed formula for both waves

Use the wave speed formula to express the frequency of light waves (f_l) and sound waves (f_s) in terms of their speeds and wavelengths: For light waves: v_l = f_l λ_l For sound waves: v_s = f_s λ_s
04

Relate the two equations and solve for the frequency ratio of light and sound waves

As λ_l = λ_s, we can divide the light wave equation by the sound wave equation: ( v_l = f_l λ_l ) / ( v_s = f_s λ_s ) Which simplifies to: (v_l / v_s) = (f_l / f_s) We know that (v_l / v_s) = 1,000,000, so: 1,000,000 = (f_l / f_s)
05

Interpret the result and find the correct answer.

This result shows that the frequency of the light wave is a million times greater than the frequency of the sound wave. Therefore, the correct answer is: d) The frequency of the light wave will be about a million times greater than that of the sound wave.

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Most popular questions from this chapter

A small ball floats in the center of a circular pool that has a radius of \(5.00 \mathrm{~m}\). Three wave generators are placed at the edge of the pool, separated by \(120 .\). The first wave generator operates at a frequency of \(2.00 \mathrm{~Hz}\). The second wave generator operates at a frequency of \(3.00 \mathrm{~Hz}\). The third wave generator operates at a frequency of \(4.00 \mathrm{~Hz}\). If the speed of each water wave is \(5.00 \mathrm{~m} / \mathrm{s}\), and the amplitude of the waves is the same, sketch the height of the ball as a function of time from \(t=0\) to \(t=2.00 \mathrm{~s}\), assuming that the water surface is at zero height. Assume that all the wave generators impart a phase shift of zero. How would your answer change if one of the wave generators was moved to a different location at the edge of the pool?

The largest tension that can be sustained by a stretched string of linear mass density \(\mu\), even in principle, is given by \(\tau=\mu c^{2},\) where \(c\) is the speed of light in vacuum. (This is an enormous value. The breaking tensions of all ordinary materials are about 12 orders of magnitude less than this.) a) What is the speed of a traveling wave on a string under such tension? b) If a \(1.000-\mathrm{m}\) -long guitar string, stretched between anchored ends, were made of this hypothetical material, what frequency would its first harmonic have? c) If that guitar string were plucked at its midpoint and given a displacement of \(2.00 \mathrm{~mm}\) there to produce the fundamental frequency, what would be the maximum speed attained by the midpoint of the string?

A \(50.0-\mathrm{cm}\) -long wire with a mass of \(10.0 \mathrm{~g}\) is under a tension of \(50.0 \mathrm{~N}\). Both ends of the wire are held rigidly while it is plucked. a) What is the speed of the waves on the wire? b) What is the fundamental frequency of the standing wave? c) What is the frequency of the third harmonic?

A \(3.00-\mathrm{m}\) -long string, fixed at both ends, has a mass of \(6.00 \mathrm{~g}\). If you want to set up a standing wave in this string having a frequency of \(300 . \mathrm{Hz}\) and three antinodes, what tension should you put the string under?

Noise results from the superposition of a very large number of sound waves of various frequencies (usually in a continuous spectrum), amplitudes, and phases. Can interference arise with noise produced by two sources?
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