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Chapter 11: Problem 59

What is the wavelength of the radio waves transmitted by an FM station at 90 MHz? (Radio waves travel at \(3.0 \times 10^{8} \mathrm{m} / \mathrm{s} .\)

Short Answer

Expert verified
Answer: The wavelength of the radio waves transmitted by an FM station at 90 MHz is 3.33 meters.

Step by step solution

01

Write down the wave speed formula

The wave speed formula is: speed = frequency × wavelength or v = f × λ Where v is the speed of the radio waves, f is the frequency of the radio waves, and λ is the wavelength of the radio waves.
02

Rearrange the formula to solve for wavelength

To find the wavelength, we need to rearrange the equation: λ = v / f
03

Convert the given frequency to Hz

The frequency is given in MHz, which is megahertz. We need to convert it to hertz (Hz) for our calculations: 90 MHz = 90 × 10^6 Hz
04

Plug in given values and solve for wavelength

Now, we can plug in the values for the speed of radio waves (v = 3.0 × 10^8 m/s) and frequency (f = 90 × 10^6 Hz) into the rearranged equation: λ = (3.0 × 10^8 m/s) / (90 × 10^6 Hz)
05

Calculate the wavelength

Now, we can perform the calculation: λ = (3.0 × 10^8 m/s) / (90 × 10^6 Hz) = (3.0 / 90) × 10^2 m = 0.033 × 10^2 m = 3.33 m The wavelength of the radio waves transmitted by an FM station at 90 MHz is 3.33 meters.

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Most popular questions from this chapter

A transverse wave on a string is described by the equation $y(x, t)=(2.20 \mathrm{cm}) \sin [(130 \mathrm{rad} / \mathrm{s}) t+(15 \mathrm{rad} / \mathrm{m}) x].$ (a) What is the maximum transverse speed of a point on the string? (b) What is the maximum transverse acceleration of a point on the string? (c) How fast does the wave move along the string? (d) Why is your answer to (c) different from the answer to (a)?
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Deep-water waves are dispersive (their wave speed depends on the wavelength). The restoring force is provided by gravity. Using dimensional analysis, find out how the speed of deep-water waves depends on wavelength \(\lambda\), assuming that \(\lambda\) and \(g\) are the only relevant quantities. (Mass density does not enter into the expression because the restoring force, arising from the weight of the water, is itself proportional to the mass density.)
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