What is the Path Difference: Waves

In summary, the question asks for the path difference (in wavelengths) between two in-phase speakers 4.50 m apart emitting 1690 Hz sound waves into a room with a speed of sound of 343 m/s. The point of interest is 8.50 m in front of one of the speakers, perpendicular to the plane of the speakers. The solution involves using the hypotenuse equation to find the path difference in meters and then converting it to wavelengths.
  • #1
ixerr
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Homework Statement


Two in-phase speakers 4.50 m apart in a plane are emitting 1690 Hz sound waves into a room where the speed of sound is 343 m/s. Consider a point that is 8.50 m in front of one of the speakers, perpendicular to the plane of the speakers. What is the path difference (in wavelengths) between the two sound waves at this point?


Homework Equations


Hypotenuse Equation...


The Attempt at a Solution


Since the speakers are 4.50 m apart, and the point is perpendicular to one of the speakers, it essentially makes the shape of a triangle. I find the hypotenuse, which is 9.6178 m, and then subtract 8.50 m from it to find the path difference. But that answer is not right :( What should I be doing..?
 
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  • #2
You've got the path difference in meters, but the question asks for the path difference in wavelengths. You're halfway there.
 

1. What is the path difference between two waves?

The path difference between two waves is the difference in distance traveled by each wave from their respective sources to a specific point. It is usually measured in terms of wavelength and is an important concept in understanding wave interference patterns.

2. How does path difference affect wave interference?

The path difference between two waves determines whether they will interfere constructively (resulting in a larger amplitude) or destructively (resulting in a smaller amplitude). When the path difference is a whole number multiple of the wavelength, the waves will interfere constructively, while a path difference of half a wavelength will result in destructive interference.

3. Can path difference be negative?

Yes, path difference can be negative if one wave has traveled a shorter distance than the other. This can occur when one wave has bounced off a reflective surface, causing it to travel a shorter distance compared to the other wave.

4. How is path difference related to the concept of phase difference?

Path difference and phase difference are closely related. Phase difference refers to the difference in the starting point or phase of two waves, while path difference refers to the difference in distance traveled. Path difference can be calculated from the phase difference by dividing it by 360 degrees and multiplying it by the wavelength.

5. Why is path difference important in determining the properties of waves?

Path difference is important in determining the interference and diffraction patterns of waves, which can provide information about the properties of the waves and the medium they are traveling through. It is also essential in understanding the behavior of waves in different situations, such as in double-slit experiments and in the formation of standing waves.

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