wavelenght in interference

Wavelength of radio wave = 3x10^8/60x1^6 m = 5 m

The signal is minimum when destructive interference occurs,
i.e path difference = (m + 1/2)入
where m is an integer and 入 is the wavelength of the radio wave

Consider the destructive interference at point A,
(QA - PA) = (m + 1/2).入 -------------------- (1)
But (PA) + (QA) = 15
i.e. QA = 15 - (PA)
Hence, equation (1) becomes,
15 - 2(PA) = (m + 1/2).入
2(PA) = 15 - m.入 - 入/2 ----------------------- (2)

Now, consider the destructive interference at point B,
(QB - PB) = (m - 1 +1/2).入 -------------------- (3)
But (PB) + (QB) = 15
i.e. QB = 15 - (PB)
Hence, equation (3) becomes,
15 - 2(PB) = (m - 1+1/2).入
2(PB) = 15 - m.入 + 入/2 ---------------------- (4)

(4) - (2): 2[(PB) - (PA)] = 入
i.e. 2(AB) = 入 = 5 m
(AB) = 5/2 m = 2.5 m










2012-01-25 11:54:18 補充：
Q: why is distance AB not equal to one wavelenght?
A: It is clear from the calculation that between two sucessive destructive interference, there is a shift of one wavelength ....

2012-01-25 11:56:25 補充：
This when PA is lengthened by 入/2, QA is automatically shortened by the same amount of 入/2, making altogether a shift of 入 for the two waves.

distance AB not equal to one wavelength
but equal to half wavelength.

because A and B are two minimum interference