Wave Interference Angle Calculation

[wilson_chem90]

Homework Statement

A two-point source operates at a frequency of 1.0 Hz to produce an interference pattern in a ripple tank. The sources are 2.5 cm apart and the wavelength of the waves is 1.2 cm.

Calculate the angles at which the nodal lines in the pattern are far from the sources. (Assume the angles are measured from the central line of the pattern).

Relevant equations:
dsinO = (n-1/2)(wavelength)

O = angle theta

The Attempt at a Solution

my problem is that i can't figure out how many nodal lines there are in order to do the question. I know once i rearrange the equation i can find the angle, by the way i rearranged it to be O = sin inverse [(n-1/2)(wavelength)/d}.

 

[Delphi51]

Just go on n = 1, 2, 3, ... until your calculator blows up!
(that is, until you get a sine value greater than 1).
You must have missed drawing all those crest circles and interference lines in high school. You can actually see a pattern and get a formula for the number of lines. I think it is 4 times the number of wavelengths of separation, counting both destructive and constructive lines.

 

[wilson_chem90]

Sorry, I'm still not following unfortunately..

 

[Delphi51]

dsin A = (n-1/2)(wavelength)
sin A = (n-1/2)(wavelength)/d
A = inverse sin[(n-1/2)(wavelength)/d]
When n = 1, A = invSin(1/2*1.2/2.5) = invSin(0.24) = 13.9 degrees
When n = 2, ...

 

[wilson_chem90]

ohh okay i thought that's what you meant. So i honestly just keep doing that until i get to a whole number?

 

[Delphi51]

Yes, keep going. You'll know when to stop.