An FM station broadcasts music at 93.5 MHz (megahertz, or 10^6 Hz ). Find the wavelength (in m,

step 1 Hi everyone, I'm here with Problem 8 from Chapter 7. In this problem, we have a radio tower that

An FM station broadcasts music at 93.5 MHz (megahertz, or...

Key Concepts

Unit Conversion

Unit conversion involves changing a measurement from one unit to another using appropriate conversion factors. In the context of wavelength calculation, converting between meters, nanometers, and angstroms is necessary to express the wavelength in different scales, where 1 meter equals 10^9 nanometers and 1 meter equals 10^10 angstroms.

Wave Equation

The wave equation, expressed as c = ?f, relates the speed of a wave (c) to its wavelength (?) and frequency (f). This fundamental relation allows one to calculate any one of these parameters if the other two are known.

Speed of Light

The speed of light is the constant speed at which electromagnetic waves, including radio waves, propagate in a vacuum—approximately 3.00 x 10^8 meters per second. This constant is crucial for linking frequency and wavelength through the wave equation.

Frequency

Frequency represents the number of cycles or oscillations that occur per unit time, and it is measured in Hertz (Hz). It is inversely proportional to wavelength in the context of wave propagation, such that as frequency increases, wavelength decreases for a given wave speed.

Wavelength

Wavelength is the distance over which the wave's shape repeats, typically measured as the distance between consecutive crests or troughs. It is a fundamental characteristic of waves and directly relates to other wave properties such as frequency and speed.

Transcript

00:01 Hi everyone, i'm here with problem 8 from chapter 7.

00:04 In this problem, we have a radio tower that is giving off waves at a frequency of 93 meghertz.

00:11 And we want to figure out what this frequency is equal to in wavelength.

00:17 So how can we do that? well, first, let's take a look at our relationships.

00:22 We know that these waves are traveling at a speed of 3 times 10 to the 8 meters per second.

00:31 And that's the speed of light.

00:35 And in this problem, we're also going to represent frequency as new.

00:40 That is a v with the hook.

00:44 And that's typically in hertz or 1 over second.

00:47 And then we'll also represent wavelength as lambda, which typically looks like an upside -down y.

00:54 And that's in meters.

00:57 So now we have to relate these three things somehow.

01:01 Well, if you notice, the speed of light is in meters per second.

01:05 And we also have two other variables that can give us exactly meters per second.

01:12 So now let's set up an equation where c, our speed of light, is equal to lambda times new.

01:26 And if we write the same equation using their units, we'll find that this is also equal to meters times 1 over second, which is exactly what the speed of light is.

01:41 And now we can rearrange this equation to give us the wavelength by taking c divided by new.

01:53 And now we can plug in our known values, which is the speed of light, three times 10 to the eighth meters per second divided by the frequency, which is 93 megahertz...

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