At what distance x do the waves have a phase difference of ___?

[FearlessRose]

1. The figure shows two point sources S1 and S2 that emit sound of wavelength λ = 1.8 m. The emissions are isotropic and in phase, and the separation between the sources is d = 18.0 m. At any point P on the x axis, the wave from S1 and the wave from S2 interfere. Start with P very far away (x = infin). As you then move P in along the x axis toward the origin, (a) does the phase difference between the waves increase or decrease? At what distance x do the waves have a phase difference of (b) 0.50λ, (c) 1.00λ, and (d ) 1.50λ?
The diagram: (d is the distance from S1 to S2)
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S1---------P-----> x
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S2
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2. Fully Destructive interference phi = (2m+1)pi, Fully constructive interference phi=m(2pi), deltaL=sqrt(324+x^2)-x

The Attempt at a Solution

Using the above equation of deltaL=sqrt(324+x^2)-x, I obtained the answers 161.5m, 80m, and 52.5 meters. sqrt(324+x^2) - x= 1 ,sqrt(324+x^2)-x=2, and sqrt(324+x^2)-x= 3

I'm confused as to why my answers are incorrect, I thought when the phase constants were 0.5lambda,1lambda, and 1.5lambda, the distance associated with these were 1,2, and 3. I know that my equation is correct from pythag, but I am not 100% sure about my x value. Any assistance is greatly appreciated. Thanks in advance.

 

[mfb]

The formulas look right, but the x-values you got as solutions are not.
Did you use a wave-length of 2 meters? It is just 1.8 m.

 

[FearlessRose]

I was looking at an example which had the wave-length as 2 meters, I must have gotten confused. Can you point me in the right direction for solving it with the 1.8m wave-length? I'm honestly confused on what to do with the wavelength.

 

[FearlessRose]

Thank you, I think I understand what I did wrong, hopefully my answers come out correct, will update after trying my hypothesis. :)

 

[FearlessRose]

All good to go, if you don't mind helping me with another problem or do I have to create another thread?

In the figure, a sound of wavelength 0.600 m is emitted isotropically by point source S. Sound ray 1 extends directly to detector D, at distance L = 10.5 m. Sound ray 2 extends to D via a reflection (effectively a "bouncing") of the sound at a flat surface. The reflection occurs on a perpendicular bisector to the SD line, at distance d from the line. Assume that the reflection shifts the sound wave by 0.500λ. For what least value of d (other than zero) do the direct sound and the reflected sound arrive at D (a) exactly out of phase and (b) exactly in phase?https://lh3.googleusercontent.com/_dJMwd_fip0l2qz4ROFS2yGDmDHDOlbuocHrTT19P1MacDMIG57SvsTuYlinwSdh22fIFMk=s170
Relevant equations: the afore mentioned equations

Attempt: I'm honestly not sure where to even start, if you could point me in the correct direction, please and thanks in advance.

 

[MaxwellsCat]

So first try thinking about exactly what out of phase and in phase mean. Then, you should be able to calculate how much of a wavelength is required for each condition and use triangles find what $d$ has to be. You know how far it has to go, written in terms of $d$, just solve for $d$.

So for example:
Ray 2 has to travel $\sqrt{{\frac{L}{2}}^2 + d^2}$, then it gets shifted by $0.5λ$, then it has to travel the same distance again.

That help?

 

[FearlessRose]

Yes, thank you so very much!

 

[berkeman]

or do I have to create another thread?

FYI, it usually works best if you create a new thread for each new question that you want help with.

 

[FearlessRose]

Thanks, as you can tell,I am a "starter"