# Calculating Smallest Path Length Difference for Overlapping Waves at Nodal Point

• rrosa522
In summary, the problem is asking for the smallest difference in path length between two point sources vibrating in phase and producing waves with a wavelength of 2.5 m. This difference can be calculated using the equation sinθn= (n-1/2) (λ/d), which relates the path length difference to the wavelength and distance between the sources. It is important to understand the concepts of sources, nodal points, and path length difference in order to solve this problem. For more information, refer to the article on path length difference provided.

## Homework Statement

Two point sources, S1 and S2, are vibrating in phase and produce waves with a wavelength of 2.5 m. The two waves overlap at a nodal point. Calculate the smallest corresponding difference in path length for this point.

## The Attempt at a Solution

I really don't know how to start this question. How can I find the length when I am only given the wavelength

What relevant equations do you think you would need?

rpthomps said:
What relevant equations do you think you would need?
sinθn= (n-1/2) (λ/d) , honestly I really don't understand what this question is asking

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Do you know what sources are, nodal points and the paths from the sources to the point on the nodal line?

rpthomps said:
Do you know what sources are, nodal points and the paths from the sources to the point on the nodal line?
yes

There is a relationship which shows that the length of a line from a point on nodal line n, to source 1 and the length of another line from the same point on nodal line n, to source 2, when subtracted have a value dependent on the wavelength of the sources. Do you remember learning about path length difference?

## What is a two point source?

A two point source is a system where two separate sources emit waves of the same frequency and amplitude, creating an interference pattern.

## What is the difference between a two point source and a single point source?

A single point source emits waves in all directions, while a two point source emits waves in specific directions that interfere with each other.

## How does the distance between the two point sources affect the interference pattern?

The distance between the two point sources affects the spacing of the interference pattern, with smaller distances creating a wider pattern and larger distances creating a narrower pattern.

## What is the principle of superposition in relation to two point sources?

The principle of superposition states that when two or more waves overlap, the resulting wave is the sum of the individual waves. In the case of two point sources, the resulting interference pattern is a combination of the two individual waves.

## How is the intensity of the interference pattern affected by the relative phase of the two point sources?

The relative phase between the two point sources can either enhance or cancel out the intensity of the interference pattern. When the waves are in phase, the interference pattern is enhanced, while when the waves are out of phase, the interference pattern is canceled out.