A. An FM radio station broadcasts at a frequency of 101.3...

Key Concepts

Unit Conversion

Unit conversion is an important concept, especially when converting between units such as megahertz to hertz for frequency or utilizing units consistently across calculations. Correct conversions ensure the wave equation is applied properly without unit mismatch.

Wave Equation

The wave equation relates the speed of a wave to its frequency and wavelength through the relationship v = ?f. This fundamental principle applies to all wave types, whether electromagnetic or mechanical, and is essential for calculating one property when the other two are known.

Frequency

Frequency is the number of oscillations or cycles that occur per unit time, usually measured in hertz (Hz). It is a key parameter in describing waves and is inversely related to the wavelength when the speed of the wave is constant.

Wavelength

Wavelength is the distance between two consecutive points in phase on a wave, such as crest to crest or trough to trough. It is a crucial characteristic of a wave and directly connects to its frequency and speed through the wave equation.

Electromagnetic Waves

Electromagnetic waves, such as radio waves, propagate at the speed of light in a vacuum (approximately 3 x 10^8 m/s). Their study involves understanding how frequencies and wavelengths interact under the constraints of the universal constant speed of light.

Speed of Sound in Air

The speed of sound in air is the rate at which sound waves travel through the medium, which at around 20°C is approximately 343 m/s. This value is dependent on temperature and is used to determine the wavelengths of sound waves for a given frequency.

Transcript

00:02 So once again, welcome to a new problem.

00:05 We're dealing with a new selection.

00:07 And a lot of people have love for radio stations.

00:12 You know, radio goes way back where based on specific frequencies, people can listen to their favorite musicians or favorite broadcasters.

00:25 And so if you think about an fm radio station, that's a specific frequency that you're dealing with.

00:35 And the frequency you're dealing with in this instance is 101 .3 megahats.

00:45 So there's broadcasting going on.

00:48 We still have waves that are needed to broadcast from one location to the other one.

00:57 So if you're listening to your radio station, your favorite radio station, the reason the reason why that's happening is because you've tuned into a specific frequency.

01:09 So this is an fm broadcasting.

01:12 We have 1 .1 .3 megahats.

01:16 Sometimes you hear, they say, oh, 101 .3 the beat or something like that.

01:22 So we want to find the wavelength that's connected to this frequency.

01:28 That's the first part of the problem we're dealing with.

01:31 So we're going to go ahead and see that if we have a a frequency of 1 .1 .3 megahertz, we can change that to hearts and that's because 10 to the 6 hearts is the same as 1 mega heart.

01:59 And so f becomes 101 .3 times 10 to the 6 hearts.

02:06 That's what we're dealing with right there.

02:09 And then we move ahead and see, that since the signal for the radio station, it's electromagnetic signal, it's going to have a velocity c which is 10 to the 8 times, 10 to the 8 meters per second.

02:34 That's the velocity would give me.

02:36 So if v is f lambda and we wanted to find lambda, we'd have to divide both sides by the frequency.

02:44 And so our lambda for the fn radio station is a v of f and v is three times 10 to the eight meters per second.

02:56 And we just transformed the frequency to hearts...

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