A radio station's channel, such as 100.7 FM or 92.3 FM, is actually its frequency in megahertz (MHz), where 1MHz=106Hz and 1Hz=1s-1. Calculate the broadcast wavelength of the radio station 91.10 FM. Express your answer to four significant figures and include the appropriate units.

3.293 m

Explanation:

Data Given:

Frequency of radio wave = 91.10 FM or 91.10 MHz

1 MHz = 10⁶ Hz

1 Hz = 1 s⁻¹

wavelength = ?

Solution:

As Frequency of radio wave is 91.10 FM or 91.10 MHz

if we look for conversion of MHz to Hz

So,

1 MHz = 10⁶ Hz

91.10 MHz = (91.10) (10⁶) = 91.1 x 10⁶ Hz

So

91.10 MHz = 91.1 x 10⁶ Hz

Now we look for conversion of Hz to s⁻¹

1 Hz = 1 s⁻¹

91.1 x 10⁶ Hz = 91.1 x 10⁶ s⁻¹

So

91.1 x 10⁶ Hz = 91.1 x 10⁶ s⁻¹

Now equation used to calculate wavelength

f = c/λ

rearrange the above equation

λ = c/f ... (1)

Where:

c = speed of light = 3 x 10⁸ ms⁻¹

λ = wavelength

put the values in above equation 1

λ = 3 x 10⁸ ms⁻¹ / 91.1 x 10⁶ s⁻¹

λ = 3.293 m

So the wavelength of radio station wave = 3.293 m