Question
Asked Feb 11, 2020
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(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.)

 

33.0 m away from each other, producing signals that are completely in phase. An avid fan of this
A radio station, broadcasting at 93.1 MHz on the FM dial, has two transmission towers d
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.
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33.0 m away from each other, producing signals that are completely in phase. An avid fan of this A radio station, broadcasting at 93.1 MHz on the FM dial, has two transmission towers d 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.

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Expert Answer

Step 1

The relation between wavelength and frequency is given by,

Advanced Physics homework question answer, step 1, image 1

Here, c is the speed of light.

From the above equation, the wavelength of the broadcasting signal is,

Advanced Physics homework question answer, step 1, image 2

Step 2

Consider the diagram for the given conditions.

Advanced Physics homework question answer, step 2, image 1

Let us suppose that the destructive interference will occur at the distance x from the closest tower.

And for the destruction of the signal, the value of the difference in wave travel should be equal to half of the wavelength.

Thus,

Advanced Physics homework question answer, step 2, image 2

Substitute the known values in the above equation.

Advanced Physics homework question answer, step 2, image 3

...

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