Destructive interference Problem

[patrickmoloney]

Homework Statement

two point sources A and B generate sinusoidal waves in a water surface. The sources are 6.0 cm apart and vibrate in phase with the same amplitude and frequency. Points of destructive interference are observed on AB, the line joining the two sources. the two nearest such points to source A occur 0.6 cm and 2.2 cm from it. determine the wavelength of the water waves. How many points of destructive interference are there in total along the line AB

Homework Equations

y₁= Asin(kx₁-ωt+ \Phi )

y₂= Asin(kx₂-ωt+ \Phi )

Superposition Principle : y= y₁+y₂

y= 2A[sin(kx₁+kx₂/2-ωt+ \Phi )cos(kx₁-kx₂/2)

The Attempt at a Solution

Have no idea. I've been at it for ages..my attempts have conjured up nothing.

 

[berkeman]

From a PM exchange -- Patrick has made progress on this question...

I know that path difference between 2 nodes is one wavelength, perhaps if A goes to b you increase distance by 1.6 cm? of and then decrease B from A by 1.6 cm. Then add these two distances and that is the wavelenght? Thanks a million! You helped me solve it. Wavelength is 3.2 cm with 4 points of destructive interference, of course! How could I have been so dumb.. 0.6, 2.2, 3.8 and 5.4 ...it all makes sense now. Thank you again.