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Chapter 7: Problem 40

An FM radio station broadcasts at \(99.5 \mathrm{MHz}\). Calculate the wavelength of the corresponding radio waves.

Short Answer

Expert verified
The wavelength of the radio waves emitted by the FM radio station broadcasting at 99.5 MHz is approximately \(3.015 * 10^3\) meters.

Step by step solution

01

Convert the frequency to Hertz

The frequency of the radio station is given in MHz. To convert this to Hertz (Hz), multiply by 1,000,000: f = 99.5 MHz * 1,000,000 = 99,500,000 Hz
02

Use the speed of light formula to find the wavelength

Now that we have the frequency in Hertz, we can use the formula λ = c / f to find the wavelength. The speed of light (c) is approximately 3.0 * 10^8 m/s: λ = (3.0 * 10^8 m/s) / (99,500,000 Hz)
03

Calculate the wavelength

Perform the division to find the wavelength: λ ≈ (3.0 * 10^8 m/s) / (99,500,000 Hz) ≈ 3.015 * 10^3 meters
04

Write the final answer

The wavelength of the radio waves emitted by the FM radio station broadcasting at 99.5 MHz is approximately 3.015 * 10^3 meters.

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