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Chapter 11: Problem 15

The speed of sound in air at room temperature is \(340 \mathrm{m} / \mathrm{s}\) (a) What is the frequency of a sound wave in air with wavelength $1.0 \mathrm{m} ?$ (b) What is the frequency of a radio wave with the same wavelength? (Radio waves are electromagnetic waves that travel at $3.0 \times 10^{8} \mathrm{m} / \mathrm{s}$ in air or in vacuum.)

Short Answer

Expert verified
Answer: The frequency of the sound wave is 340 Hz, and the frequency of the radio wave is 3.0 x 10^8 Hz.

Step by step solution

01

Write down the known values

We have the following known values: (a) Sound wave - Speed: \(340 \mathrm{m/s}\), Wavelength: \(1.0 \mathrm{m}\) (b) Radio wave - Speed: \(3.0 \times 10^8 \mathrm{m/s}\), Wavelength: \(1.0 \mathrm{m}\)
02

Write the formula for the relationship between speed, wavelength, and frequency

The formula is: Speed = Wavelength x Frequency
03

Calculate the frequency of the sound wave

Using the formula and the given values, we can find the frequency of the sound wave: Frequency = Speed / Wavelength Frequency = \(340 \mathrm{m/s} / 1.0 \mathrm{m}\) Frequency = \(340 \mathrm{Hz}\) So the frequency of the sound wave is \(340 \mathrm{Hz}\).
04

Calculate the frequency of the radio wave

Now we will use the same formula and the given values to find the frequency of the radio wave: Frequency = Speed / Wavelength Frequency = \((3.0 \times 10^8 \mathrm{m/s}) / 1.0 \mathrm{m}\) Frequency = \(3.0 \times 10^8 \mathrm{Hz}\) So the frequency of the radio wave is \(3.0 \times 10^8 \mathrm{Hz}\). In conclusion, the frequency of the sound wave in air with a wavelength of \(1.0 \mathrm{m}\) is \(340 \mathrm{Hz}\), and the frequency of a radio wave with the same wavelength is \(3.0 \times 10^8 \mathrm{Hz}\).

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Most popular questions from this chapter

What is the speed of the wave represented by \(y(x, t)=\) $A \sin (k x-\omega t),\( where \)k=6.0 \mathrm{rad} / \mathrm{cm}\( and \)\omega=5.0 \mathrm{rad} / \mathrm{s} ?$
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While testing speakers for a concert. Tomás sets up two speakers to produce sound waves at the same frequency, which is between \(100 \mathrm{Hz}\) and $150 \mathrm{Hz}$. The two speakers vibrate in phase with one another. He notices that when he listens at certain locations, the sound is very soft (a minimum intensity compared to nearby points). One such point is \(25.8 \mathrm{m}\) from one speaker and \(37.1 \mathrm{m}\) from the other. What are the possible frequencies of the sound waves coming from the speakers? (The speed of sound in air is \(343 \mathrm{m} / \mathrm{s} .\) )
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