(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given two isotropic point sources of sound [itex]\[s_{1}\][/itex] and [itex]\[s_{2}\][/itex]. The sources emit waves in phase at wavelength 0.50m; they are separated by D = 1.75m. If we move a sound detector along a large circle centered at the midpoint between the sources, at how many points do waves arrive at the detector (a) exactly in phase, and (b) exactly out of phase?

2. Relevant equations

When the ratio of [itex]\[\frac{\Delta L}{\lambda }\][/itex] is 0, 1, 2, or integral multiple of

[itex]\lambda[/itex], we have a fully constructive interference. When the ratio is odd multiple of [itex]\lambda[/itex] (thus, ratio is 1/2, 3/2, 5/2...etc), we have fully destructive interference.

3. The attempt at a solution

The answers to both are 14.

This is what I had initially.... assuming r >>> D

It should be positive to say that [itex]\[s_{1}\][/itex] and [itex]\[s_{2}\][/itex] is constructive at point a, because the both will travel at identical path length.

At point b, the difference should always be 1.75m, because [itex]\[s_{2}\][/itex] has to travel an additional 1.75m (the distance of which the two sources are separated).

--edited---

but 7/2 is neither fully constructive nor fully destructive right??? am i correct???

Then I am lost with how to get 14 of them. I know both have 14 because of the symmetry. But what points should I label on the circle???

I was looking up on the Internet, and we have to get the ratio, 1.75/0.5 = 3.5, and this means 7/2. But I am confused.

I know that [itex]\[L_{1} - L_{2} = n \lambda \][/itex] (constructive). What does this ratio, n, means at all???

Similarly, for destructive, we have [itex]\[L_{1} - L_{2} = (n+\frac{1}{2} )\lambda \][/itex], and n (the ratio) is 3.

How do we use the ratio, n, to solve this problem (or any interference of sound wave problems?) What is the game plan for solving any interference problems?

I appreciate any helps! Thanks

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# Sound wave interfernce on a large circle

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