Destructive Interference problem

[jhoffma4]

The problem states:

Waves broadcast by a 1152 kHz radio sta-
tion arrive at a home receiver by two paths.
One is a direct path, and the second is from
re°ection o® an airplane directly above the re-
ceiver. The airplane is approximately 137 m
above the receiver, and the direct distance
from station to home is 18:7 km.
What is the height (within 1% error) of the
airplane if destructive interference occurrs?
Assume no phase change on reflection.
Answer in units of m.

First of all I am kind of confused as to where the receiver is...on the house or the radio station. I was thinking it should be on the house, but 137 meters seems very low for an airplane to be flying above a house.

What I know/tried:
I know that since it's destructive interference, it is out of phase, so we use ∆L=(lamda/2). and we can find L1 and L2 with the values given, but I have no idea how to include frequency...maybe using v=lamda/f? I tried applying the small angle approximation (where sinө~tanө), but the trigonometry is really confusing and I wasn't having much success. Could someone help?

 

[tiny-tim]

Hi jhoffma4!

First of all I am kind of confused as to where the receiver is...on the house or the radio station. I was thinking it should be on the house, but 137 meters seems very low for an airplane to be flying above a house.

It doesn't matter, does it?

… but I have no idea how to include frequency...maybe using v=lamda/f? I tried applying the small angle approximation (where sinө~tanө), but the trigonometry is really confusing and I wasn't having much success. Could someone help?

Yes, v=lamda/f should do fine.

And just use Pythagoras.