Phase difference equation.

In summary, the conversation is about a problem involving two loud speakers, a listener, and an oscillator. The question is to find the phase difference between two waves reaching the listener, and the frequency to which the oscillator can be adjusted for minimal sound. The solution involves finding the difference in distance between the two speakers and the listener, using the formula [lamb] = v/f to find the wavelength, and then using the equation [psi] = .61m / 1.143m * 2[pi] to find the phase difference. For part B, the amplitude of the waves needs to be taken into consideration, but as no information is given, it is sufficient to solve for [psi] = [pi].
  • #1

Jenn_Lane2001

Hi i posted here before and got great help, and I ran into another problem maybe you can help me this is the question.

Two loud speakers are placed on a wall 2.00 m apart. A listener stands 3.00m from the wall direclty infront of one of the speakers. A single ocillator is driving the speakers in phase at a frequency of 300Hz.
A. What is the phase difference between tehe two waves when they reach the observer.
B. What is the frequency closest to 300 hz. to which the oscillator may be adjusted such that the observer hears minimal sound?

This is what I did..

r1= square root of (3.00)^2 = 3
r2= square root of ((3.00)^2 + (2.00)^2) = 3.61

The difference is = r2-r1 = .61

Now this is where i got stuck I wasnt sure if i had to use .61/2pie to find the phase difference.
Also what forumla should I use for part B.
Thank you in advance.
 
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  • #2
Hi Jenn_Lane2001,
I think you got the difference in distance correctly. Next you should find out what the wavelength is for a 300Hz sonic wave.
 
  • #3
R u sure..?

I didnt think you need to know the wavelength. more the velocity but that is what i wasnt sure calculating. I am not sure of the equation to use. Thanks
 
  • #4
[lamb] = v/f,
where
[lamb] is wavelength
v is velocity
f is frequency
I think, for sonic waves, v = 340 m/s or something.
 
  • #5
Oh ok so sonic is the speed of sound

the speed of sound is 343v and then you will divide that by frequency which is 300 hz which equals wavelength= 1.143. now that i have the wavelenght where would i put taht into use as to determine the answers. Thanks a lot for the help.
 
  • #6
Right. Since the progress in phase is 2[pi] for each wavelength travelled, your phase difference is
[psi] = .61m / 1.143m * 2[pi].
That's the answer to A.

Part B is more difficult. You know two waves cancel out each other when [psi] = [pi]. But that's only true if amplitudes are equal. You know the amplitude decreases (sound becomes softer) as you move away from a speaker. So the speaker that is more distant from the observer has to be turned up a bit if you want waves to cancel out. Anyway, as no info about amplitudes is given in the problem, it will probably do to solve for [psi] = [pi].
 

What is the phase difference equation?

The phase difference equation is a mathematical relationship that describes the difference in phase between two waves. It is typically represented as Δϕ = ϕ2 - ϕ1, where Δϕ is the phase difference, ϕ2 is the phase of the second wave, and ϕ1 is the phase of the first wave.

How is the phase difference equation used?

The phase difference equation is used to calculate the phase difference between two waves. This information is important in understanding the interference patterns of waves, as well as in various applications such as signal processing and communication systems.

What factors affect the phase difference between two waves?

The phase difference between two waves can be affected by the wavelength, frequency, and amplitude of the waves. It can also be influenced by the medium through which the waves are traveling, as well as any obstacles or obstructions in the path of the waves.

Can the phase difference be negative?

Yes, the phase difference can be negative. This occurs when the second wave is ahead of the first wave in its cycle, resulting in a negative value for the phase difference. This can happen when waves are traveling in opposite directions or when there is a phase shift between the waves.

What is the relationship between the phase difference and interference patterns?

The phase difference between two waves is directly related to the interference pattern that is created when the waves meet. When the phase difference is a multiple of 2π, the waves are said to be in phase and constructive interference occurs. When the phase difference is an odd multiple of π, the waves are said to be out of phase and destructive interference occurs.

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