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.

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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