TV-reception antennas for VHF (channels 2 through 13) are constructed with cross

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 8 and 2 and find them to be 0.827 and 2.71 m long, respectively.

What is the frequency for channel 8? For Channel 2?

Please show either how to derive the answer or how you got the answer. Thanks! You should have to use some variation of the formula ? = c/f

Explanation / Answer

For channel 8

lambda =2*0.827 =1.654 m

f =c/lambda =3*10^8/1.654

f=1.81*10^8 Hz

For channel 2

lambda =2*2.71 =5.42 m

f=c/lambda =3*10^8/5.42

f=0.55*10^8 Hz

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