TV-reception antennas for VHF (channels 2 through 13) are constructed with cross wires supported at their centers, as shown in Figure 23.24. The ideal length for the cross wires is one-half the wavelength to be received, with the more expensive antennas having one for each channel. Suppose you measure the lengths of the wires for channels 2 and 9 and find them to be 2.71 and 0.801 m long, respectively.

Question

TV-reception antennas for VHF (channels 2 through 13) are constructed with cross wires supported at their centers, as shown in Figure 23.24. The ideal length for the cross wires is one-half the wavelength to be received, with the more expensive antennas having one for each channel. Suppose you measure the lengths of the wires for channels 2 and 9 and find them to be 2.71 and 0.801 m long, respectively.
What is the frequency for channel 2?
1  Hz
What is the frequency for channel 9?
2  Hz

Elena · Answer

L = λ/2, λ = 2•L f1 = c/λ1 = c/2•L1= 3•10^8/2•2.71 =5.54•10^7 Hz f2 = c/λ2 = c/2•L2= 3•10^8/2•0.801 =1.87•10^8 Hz