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Nowadays many highway tunnels are equipped with AM \"repeaters\" so that motoris

ID: 1758449 • Letter: N

Question

Nowadays many highway tunnels are equipped with AM "repeaters" so that motorists can listen to their AM radios while inside. Otherwise, AM radio cannot be received in the tunnel. FM repeaters are not usually necessary, since FM reception in tunnels is often acceptable without any special assistance. A typical tunnel is 5 meters high. (a) What is the wavelength of the electromagnetic radiation from an FM station broadcasting at 94.1 MHz, which penetrates easily into the tunnel? (b) What is the wavelength of the electromagnetic radiation from an AM station broadcasting at 940 kHz, which ordinarily cannot penetrate into the tunnel?

Explanation / Answer

In both cases ,    wavelength = speed of light / frequency . (a)   wavelength = 3 x 108 /94.1 x 106=    3.19 meters . (b)   wavelength = 3 x 108 / 940 x103=    319meters