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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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