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Before the switch to digital television broadcasting in 2009, many people withou

ID: 1527922 • Letter: B

Question

Before the switch to digital television broadcasting in 2009, many people without cable or satellite had outdoor TV antennas. TV-antennas for VHF-Very High Frequency (channels 2 through 1 were made with perpendicular wires supported at their centers, as shown below. The ideal length for these wires one-half the wavelength of the wave that is trying to be picked up, with the more expensive antennas having one for each channel. If you measure the lengths of the wires for channels 10 and 2 and find them to be 0.457 m and 1.457 m long, respectively. What is the frequency for channel 10? What is the frequency for channel 2? Hz

Explanation / Answer

Channel 10

wavelength = length *2 = 0.457*2 = 0.91 m

Frequency = speed / wavelength = 3 * 10^8 / 0.91 = 3.29 *10 8 Hz

Channel 2

wavelength =2* length = 2*3.29 = 6.58

Frequency = speed / wavelength = 3 x 10^8 / 6.58 = 0.45* 10 ^8 Hz

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