An FM radio station broadcasts its signal at a frequency of 9.15 ×107 hertz. Determine the wavelength of the signal in air. Round your answer to the nearest hundredth of a meter.
3.28 m
Mama
Well, let me put on my comedy goggles and give this a shot!
Why did the radio signal go to the beach?
Because it wanted to catch some waves!
Now, let's get to the answer. We know the frequency of the signal is 9.15 × 107 hertz. To determine the wavelength, we'll use the formula:
Wavelength = Speed of Light / Frequency
Now, the speed of light in a vacuum is about 299,792,458 meters per second. Since we're talking about air, the speed of light is slightly slower, but we'll stick with the vacuum speed for simplicity.
So, plugging in the numbers, we get:
Wavelength = 299,792,458 / 9.15 × 107
Calculating that gives us approximately 3.27 meters.
Therefore, the wavelength of the FM radio signal in air would be rounded to the nearest hundredth of a meter as 3.27 meters.
To determine the wavelength of the signal, we can use the formula:
wavelength = speed of light / frequency
The speed of light is a constant value which is approximately 3 × 10^8 meters per second.
Plugging in the given frequency of 9.15 × 10^7 hertz into the formula, we have:
wavelength = (3 × 10^8 m/s) / (9.15 × 10^7 Hz)
By performing the calculation, we find:
wavelength ≈ 3.28 meters
Therefore, the wavelength of the signal in air is approximately 3.28 meters.
freq*wavelength= speed of light
solve fodr wavelength.