Question

you have two waves leaving 2 different sources in phanse. there is disruptive interference at point p, which is 1m away from one source and .5m away from the other. What are possible wavelengths for these waves? (please show work)

Answer 1

Condition for destructive interference is path difference = (m+0.5)*lamda,where m is any interger

for m = 0
Given that r2 = 1 m and r1 = 0.5 m

r2-r1 = (0+0.5)*lamda

lamda = 2*(r2-r1) = 2*(1-0.5) = 1 m

for m = 1

r2-r1 = (1+0.5)*lamda

(1-0.5) = (1+0.5)*lamda

(0.5/1.5) = lamda

lamda = 0.33

so for m = 2

r2-r1 = (2+0.5)*lamda

0.5 = 2.5*lamda

lamda = 0.2 m

for m = 3

0.5 = 3.5*lamda

lamda = 0.142 m

for m = 4

0.5 = 4.5*lamda

lamda = 0.11 m

for m = 5

0.5 = 5.5*lamda

lamda = 0.09 m ..and so on ,these are the possible values of wavelength