- #1

**Homework Statement**

A radio transmitting station operating at a frequency f=100 MHz has two identical antennas that radiate in phase (in other words, coherent with respect to each other). Antenna B is 10 m to the right of antenna A. Consider the point P between the antennas, and along the line connecting them a horizontal distance x to the right of antenna A.

a) What is the wavelength of the electromagnetic wave?

b) At point P, what is the path difference (PD) between the waves coming from the two antennas (give your answer in terms of x)?

c) For what values of x will constructive interference occur at point P?

d) How many constructive interference points will be there on the line between the two antennas?

**Relevant Equations**

c=λf

v=λf?

**The attempt at a solution**

a.) c=λf, so λ=(3*10

^{8}m/s)/(1*10

^{8}Hz)=3m. This gave me the correct answer according to the study guide, but I've seen some people use v (speed of sound) instead of c (speed of light). I'm not sure which is correct.

b.) PD= (10-x)-x= 10-2x

c.) Constructive interference occurs when PD= mλ. So, x=-(mλ)/20. For m values 1-4, x= -0.15, 0.3, 0.45, 0.6 According to the answer key this is wrong, but I don't understand how to get the right answer.

d.) The total distance is 10m, so I would keep plugging in m values until I get an x ≥10.