# Interference of Waves Homework: Path Length Difference & Type of Interference

• Nano
In summary, the question asks about the difference in path length between two identical sound waves arriving at a point P from two point sources S1 and S2. The waves are emitted at a frequency of 171.5 Hz and the path length difference is calculated using the equation L = λn/2. The concept of harmonics is not applicable in this problem, instead, the interference between the waves at point P is determined by dividing the path length difference by the wavelength.
Nano

## Homework Statement

Two point sources S1 and S2 emit idential sound waves of frequency 171.5 Hz as shown to the right. In terms of wavelength, what is the difference in the path length between the waves arriving at point P if
a) L1 = 38m and L2 = 34 m
b) L1 = 39m and L2 = 36m
c) Assuming that the source separation is much smaller than L1 and L2, what type of interference occurs at P in situations a and b?

*There is a picture: The paths of waves emitted from points S1 and S2 are straight lines that are converging twrds each other and intersect at P. Its sort of a triangle, w/ P at the vertex

## Homework Equations

wavelength = f *v
f = nv/2L --> n is harmonic number, but its not given?

## The Attempt at a Solution

From that 2nd equation, I worked out that
L = $$\lambda$$n/2

But I really don't understand what the question is asking. If the waves are identical, than how is their path length changed? And how do you express it "in terms of lambda"?

Last edited:
The idea behind this question is to figure out if the waves constructively interfere at point P, or destructively interfere. If the path lengths differ by a whole number of wavelengths then the waves will constructively interfere. If the path lengths differ by half wavelength, or an odd number of half wavelengths then they will destructively interfere. (Review these terms in your text if you ae not familiar with them). So you need to take your distances and divide by the wavelength to see what you've got.

The concept of harmonics goes with standing waves, but this problem isn't about standing waves.

Oh, ok thanks! It makes much more sense now. I see what the idea behind this is now, and that's what was confusing in the first place.

## 1. What is the path length difference?

The path length difference refers to the difference in distance traveled by two waves from their sources to a specific point. It is an important factor in determining the type of interference that will occur between the waves.

## 2. How does path length difference affect interference?

The path length difference is directly related to the phase difference between two waves. A greater path length difference results in a greater phase difference, which can lead to constructive or destructive interference depending on the type of waves.

## 3. What is constructive interference?

Constructive interference occurs when two waves with the same frequency and amplitude meet at a point with a path length difference that is a multiple of the wavelength. This results in a wave with a larger amplitude, which is the sum of the individual wave amplitudes.

## 4. What is destructive interference?

Destructive interference occurs when two waves with the same frequency and amplitude meet at a point with a path length difference that is an odd multiple of half the wavelength. This results in a wave with a smaller amplitude, as the waves cancel each other out.

## 5. How do you calculate the path length difference?

The path length difference can be calculated by finding the difference in distances traveled by the two waves, taking into account any reflections or refractions that may occur. This value can then be used to determine the phase difference and type of interference between the waves.

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