Television sets sometimes use a "rabbit-ears" antenna. A rabbit-ears antenna consists of a pair of metal rods. The length of each rod can be adjusted to be one-fifth of a wavelength of an electromagnetic wave whose frequency is 60.0 MHz. How long is each rod?
speed of light = wavelength x frequency.
speed of light is 3 x 10^8 meters/second.
You have the frequency (change to Hz). Calculate wavelength and take 1/5 of that.
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Electromagnetic waves travel at the speed of light
c=3×10^8m/s.
In this particular case we have that the transmitted wave has a frequency
f=60MHz=60×10^6Hz
The relationship between the frequency (f) of the electromagnetic wave and its wavelength (λ) is given by: c=fλ. Thus, solving for λ :
λ=cf=(3×10^8m/s)(60×10^6Hz)=5m
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As each rod can be adjusted to be a fifth of a wavelength, then:
rod length=15λ rod length=1/5×5m=1mTherefore, the length of each rod is
1m
To find the length of each rod of a rabbit-ears antenna, we need to first determine the wavelength of an electromagnetic wave with a frequency of 60.0 MHz. The formula to calculate wavelength is:
Wavelength = Speed of Light / Frequency
The speed of light is approximately 3.0 x 10^8 meters per second. To convert the frequency from MHz to Hz, we need to multiply it by 10^6.
Frequency in Hz = 60.0 MHz x 10^6
Now we can substitute the values into the formula:
Wavelength = (3.0 x 10^8) / (60.0 MHz x 10^6)
Wavelength = (3.0 x 10^8) / (60.0 x 10^6) meters
Wavelength = (3.0 / 60) meters
Wavelength = 0.05 meters
Now that we have the wavelength, we can calculate the length of each rod, which is one-fifth of the wavelength:
Length of each rod = 0.05 meters / 5
Length of each rod = 0.01 meters
Therefore, each rod of the rabbit-ears antenna is 0.01 meters long.