The Beat (CKBT-FM) is a radio station broadcasting at 91.5 FM in Kitchener, Ontario. 91.5 The Beat Music Station. This radio station broadcasts on a frequency of 91 MHz. What is the wavelength of the radio waves in meters? Note: MHz = 1×10^6 Hz. Enter the wavelength accurate to significant figures. For scientific notation, enter 1234 as 23e3 and 0.01234 as 23e-5.
The Correct Answer and Explanation is:
To find the wavelength (λ\lambdaλ) of the radio waves, we can use the formula: λ=cf\lambda = \frac{c}{f}λ=fc
where:
- λ\lambdaλ is the wavelength in meters,
- ccc is the speed of light in a vacuum, which is approximately 3.00×108 m/s3.00 \times 10^8 \, \text{m/s}3.00×108m/s,
- fff is the frequency of the wave in Hz.
Step 1: Convert the frequency to Hz
The radio station broadcasts at 91.5 MHz. Since 1 MHz=1×106 Hz1 \, \text{MHz} = 1 \times 10^6 \, \text{Hz}1MHz=1×106Hz, we can convert the frequency: f=91.5 MHz=91.5×106 Hz=9.15×107 Hzf = 91.5 \, \text{MHz} = 91.5 \times 10^6 \, \text{Hz} = 9.15 \times 10^7 \, \text{Hz}f=91.5MHz=91.5×106Hz=9.15×107Hz
Step 2: Calculate the wavelength
Now, we can plug the values into the formula for wavelength: λ=3.00×108 m/s9.15×107 Hz\lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{9.15 \times 10^7 \, \text{Hz}}λ=9.15×107Hz3.00×108m/s λ=3.28 m\lambda = 3.28 \, \text{m}λ=3.28m
Thus, the wavelength of the radio waves is approximately 3.28 meters.
Explanation:
The wavelength is inversely related to the frequency: higher frequencies correspond to shorter wavelengths. In this case, the radio station’s frequency of 91.5 MHz corresponds to a wavelength of about 3.28 meters. Radio waves with higher frequencies, like those in the FM band, have shorter wavelengths compared to lower-frequency waves like those in the AM band.
This wavelength is crucial in determining how radio waves propagate through the air and how antennas are designed for transmission and reception. The wavelength is typically measured in meters because it’s more practical for the radio frequencies used in broadcasting.
