If the frequency of oscillation of the wave emitted by an FM radio station is 89.8 MHz, determine the wave's wavelength.

This is what I did:

89.8 MHz = 89800000 Hz
v = lambda x f
lambda = v/f = 343 m/s/89800000 Hz = 3.82 x 10^-6 m

What am I doing wrong?

You are using the velocity of sound instead of the velocity of light. There is a considerable difference in them.

How do you know that the speed of light should be used.

I used the speed of sound because the question said, "radio station".

You have made a small mistake in your calculation. The correct answer is:

Given:
Frequency (f) = 89.8 MHz = 89.8 x 10^6 Hz

To find the wavelength (λ), we can use the formula:
v = λ x f

The speed of light (v) in a vacuum is approximately 3.00 x 10^8 m/s.

Substituting the values into the formula:

λ = v / f
= (3.00 x 10^8 m/s) / (89.8 x 10^6 Hz)
= 3.34 m

Therefore, the wavelength of the wave emitted by the FM radio station is 3.34 meters.

Your calculation to determine the wavelength of the wave emitted by the FM radio station is correct. The issue lies in the conversion factor you used for the speed of light (v).

In your calculation, you used the value of the speed of sound (343 m/s) as the velocity (v) of the wave. However, you should be using the speed of light (c) because electromagnetic waves, such as radio waves, travel at the speed of light, not the speed of sound.

The speed of light is approximately 3.00 x 10^8 meters per second (m/s).

Let's recalculate the wavelength using the correct velocity value:

f = 89800000 Hz
v = 3.00 x 10^8 m/s

Now we can use the formula:
lambda = v/f

lambda = 3.00 x 10^8 m/s / 89800000 Hz
= 3.343 x 10^(-3) m

Therefore, the wavelength of the wave emitted by the FM radio station is approximately 3.343 millimeters (mm).