Phase Difference Calculation between Two Sound Fonts: Homework Help Needed

In summary, the question is asking for the phase difference between two sound fonts producing plain harmonic waves with the same amplitude and frequency. By using the equation V=Yf, where V is the wave velocity, Y is the wave longitude, and f is the frequency, we can calculate Y to be 17/100. Using the equation Phase Difference=kr2-kr1, we can find the phase difference by substituting k=2TT/Y and r2=25 and r1=8. However, the correct answer is that the waves are in phase. This can be explained by considering the time it takes for the sound to travel from each font to a point 8m away. Since the time difference is very small, the
  • #1
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Homework Statement



Two sound fonts make plain armonic waves with the same amplitude and frequency. If f=200 Hz and V=340 m/s, the phase difference in a point situated 8m away from one font and 25 m away from the other one will be...

Homework Equations



V=Yf
Y: Wave longitude
Phase Difference=kr2-kr1 (Found it online and is so far the only one I know about)

The Attempt at a Solution



Y=V/f=340/200=17/100
TT=Pi
K=2TT/Y
K=2TT/(17/100)
Phase Difference=k(r2-r1)
P.D=(2TT/(17/100))*17
P.d=2TT*100

Nut in the answer sheet it says the answer is: The waves are in phase. Please explain why?
 
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  • #2
Here is how I would reason about the problem: Let A be the source of sound 8 meters away and B the one 25 meters away. The time it takes for you to hear A is 8/340 seconds. The time it takes for you to hear B is 25/340 seconds which is roughly 3*(8/340) seconds. Hence, the phase difference would be very small.
 
  • #3
340/200 is NOT 17/100. Please correct that, ok? You have a phase difference of 100*pi (it's not really that, but you'll correct it). 2*pi is one whole wave length. A wave shifted by 2*pi in phase is the same wave again since the wave pattern repeats every 2*pi. So a shift of 2*pi is the same as no shift at all. So if your phase shift is a multiple of 2*pi then the two sounds are 'in phase'. If you get a phase shift bigger than 2*pi then just take the remainder after dividing by 2*pi to get the phase shift.
 

FAQ: Phase Difference Calculation between Two Sound Fonts: Homework Help Needed

What is phase difference?

Phase difference is a measure of the relative shift in the position or timing of two waves. It is the difference in the phase angles of two waves at a specific point in time or space.

How is phase difference calculated?

Phase difference is calculated by finding the difference between the phase angles of two waves. This can be done by measuring the time difference between two points on the wave or by comparing the peaks or troughs of the waves.

What causes phase difference?

Phase difference can be caused by a variety of factors, such as the speed or frequency of the waves, the medium through which the waves are traveling, or any obstacles or interference that the waves encounter.

How does phase difference affect wave interference?

Phase difference plays a crucial role in determining how waves interact with each other. When waves with the same frequency and amplitude have a phase difference of 180 degrees, they cancel each other out, resulting in destructive interference. On the other hand, when waves have a phase difference of 0 degrees, they reinforce each other, resulting in constructive interference.

How is phase difference used in real life?

Phase difference is used in many real-life applications, such as audio and video technology, radio and television broadcasting, and medical imaging. It is also important in fields such as optics, acoustics, and electronics, where understanding the behavior of waves is crucial.

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