An FM radio station broadcasts at 9.23 × 107 Hz. Given that the radio waves travel at 3.00 × 108 m/s, what is the wavelength of these waves?

Hey there smarty!

Let's consider this. So, this station here, they broadcast at 9.23 × 107 Hz.

There wave travels at 3.00 × 108 m/s.

By divided them both, (which this is what we would do), we would conclude to get the answer as (3.25 m).

Hope this helps you!

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VFAbraham VFAbraham · Answer 2 · 2020-01-31T02:02:05+01:00

Answer:

The wavelength of these waves is [tex]\lambda=3.25\ m[/tex].

Explanation:

The wavelength ([tex]\lambda[/tex]) of a periodic wave is the distance between consecutive points with the same phase, like crests.

We are told that the radio station broadcasts at a frequency of [tex]f=9.23x10^{7} Hz[/tex] and that the radio waves travel at a speed of [tex]v=3.0x10^{8}\frac{m}{s}[/tex].

The wavelength ([tex]\lambda[/tex]) depends on the speed ([tex]v[/tex]) and the frequency ([tex]f[/tex]). We use the expression:

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

Replacing those values we get that

[tex]\lambda=\frac{3.0x10^{8}\frac{m}{s}}{9.23x10^{7}\frac{1}{s}}[/tex]

[tex]\lambda=3.25\ m[/tex]