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Let's say your favorite radio station is "at 99.9 on the FM dial," which means it is broadcast using electromagnetic waves with a frequency of 99.9 MHz (megahertz, or millions of hertz). What wavelength do these waves have?

Answer :

Answer:

The wavelength of the wave is 3.003 m

Explanation:

Given:

Frequency of the EM waves (f) = 99.9 MHz

Speed of the EM waves is equal to speed of light. So, [tex]v=3\times 10^8\ m/s[/tex]

First let us convert the frequency from MHz to Hz using the conversion factor.

We know, 1 MHz = 10⁶ Hz.

∴ 99.9 MHz = 99.9 × 10⁶ Hz

We know that, speed of a wave is related to its frequency and wavelength as:

Speed (v) = Frequency (f) × Wavelength (λ)

[tex]v=f\times \lambda[/tex]

Now, rewriting the above equation in terms of 'λ', we get:

[tex]\lambda=\dfrac{v}{f}[/tex]

Now, plug in the given values and solve for 'λ'. This gives,

[tex]\lambda=\frac{3\times 10^8\ m/s}{99.9\times 10^6\ Hz}\\\\\lambda=3.003\ m[/tex]

Therefore, the wavelength of the wave is 3.003 m.

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Rewritten by : Barada

The wavelength of the wave is 3.003 m

Calculation of the wavelength:

Since Frequency of the EM waves (f) = 99.9 MHz

So, the speed of the EM waves should be equivalent to the speed of the light [tex]v = 3\times ^{8}m/s[/tex]

We know that

1 MHz = 10⁶ Hz.

So, 99.9 MHz = 99.9 × 10⁶ Hz

Now

The wavelength should be

[tex]= \frac{3\times 10^{8}}{99.9 \times 10^{6}}[/tex]

= 3.003 m

This question is incomplete. Here are the missing details.

The speed of the EM waves should be equivalent to the speed of the light [tex]v = 3\times ^{8}m/s[/tex]

Learn more about frequency here: https://brainly.com/question/20038359