A radio station, broadcasting at 89.1 MHz on the FM dial, has two transmission towers d = 40.0 m away from each other, producing signals that are completely in phase. An avid fan of this station is listening to it on her portable radio while jogging directly toward one of the towers from an initially large distance away, as shown below. Let x be her distance from the closest tower.

Question

A radio station, broadcasting at 89.1 MHz on the FM dial, has two transmission towers d = 40.0 m away from each other, producing signals that are completely in phase. An avid fan of this station is listening to it on her portable radio while jogging directly toward one of the towers from an initially large distance away, as shown below. Let x be her distance from the closest tower.
A)At what distance x will the jogger first experience no radio signal, due to destructive interference?
B)The jogger stops when she gets to the bottom tower. During her jog, how many times total did she experience a loss of signal? (A whole number is required here.)

bobpursley · Answer

first. IT is FM. If the frequency is not varying, I wonder how she is "listening" to it, as it will make no sound on her radio.

FM does not use towers as antennas, the wavelengths are too short, they use short antenna arrays, which may be installed on a tower, or not. Figure the wavelength of an FM (100Mhz) or AM (1100kh) and you see why the antennnas are different.

Not the question. Interference. So if the change in position is one quarter wavelength from tower one, it must be now also a quarter wavelength change in the distance from tower two, or be 180 deg out of phase.

b. if the jogger goes another 1/4 wave, the other wavy is now 1/4 shift, so the total shift now is 1 wavelength, or in phase. Constructive nterference. Repeat that going to tower B. So you get one destructive waveldngth per 1/2 wave length of x, so how many half wavelength are between A and B?