# Distance to the nearest node along the back wall

• lodestar
In summary, two 512Hz tuning forks are placed 3.0 m apart in a classroom with a speed of sound of 343 m/s. If the back wall of the room is 10.0 m away, the distance from the back corner to the nearest node along the back wall can be found using the formula path length difference = (n-1/2)λ. The central anti-node is 3.5 m from the corner, the first node is 1.12 m from the central anti-node, and the second node is 3.35 m from the central anti-node. The third node is beyond the corner at 5.58 m. The second node is 0.15 m from the
lodestar

## Homework Statement

Two 512Hz tuning forks are placed 3.0 m apart on the bench at the front of a classroom. Each is 2.0 m from a side wall and the room is 7.0 m. The speed of sound is 343 m/s.
b) If the back wall room is 10.0 m away what is the distance from the back corner of the room to the nearest node along the back wall?

## Homework Equations

wavelength = speed/frequency
Path length difference = (n-1/2)λ

## The Attempt at a Solution

The wavelength of sound is found to be 0.67m (wavelength = 343 m/s / 512 Hz).
path length difference = x - (3.5 - x) = 2x - 3.5 m
2x - 3.5m = (n-1/2)λ
x = [(n-1/2)λ + 3.5m]/2
node = 1
x = 1.92 m

I have partial answers from my teacher. The central anti node is 3.5 m from the corner. The first node is 1.12 m from the central antinode. The second node is 3.35 m from the central anti node. The third node is 5.58 m (beyond the corner). The second node is 3.5 - 3.5 = 0.15 m from the corner. I do not understand how to find the distances of these nodes from the central anti node.

This sounds (unintentional pun) like a double slit problem.

It's just geometry. Draw a diagram of the room. Mark an antinode, say, at distance x from the central antinode. How far is it from there to each fork?

Node would be destructive interference.

It does sound like a double slit problem.

lodestar,

I think it would help you to recall two things: why there is a node centered between the two forks and the wave equation.

#### Attachments

• waves and things.docx
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• path diff.png
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Anti-node is destructive I believe.

Wily Willy said:
Anti-node is destructive I believe.
No, andrevdh is right.

T1 and T2 are the two tuning forks.
The path length difference between the two waves is the distance Δ in the drawing .
Which is (n - 1/2)λ as you mentioned.

## 1. What is a node?

A node is a point or location on a surface or object where measurements or observations are taken for analysis or study.

## 2. How is the distance to the nearest node along the back wall measured?

The distance to the nearest node along the back wall is typically measured using a measuring tape or a laser distance measurer.

## 3. Why is the distance to the nearest node along the back wall important?

This measurement is important for understanding the layout and dimensions of a space or object, as well as for planning and designing purposes.

## 4. Can the distance to the nearest node along the back wall change over time?

Yes, the distance to the nearest node along the back wall may change over time due to factors such as expansion or contraction of materials, movement of objects, or changes in the environment.

## 5. Are there any limitations to using the distance to the nearest node along the back wall as a measurement?

One limitation is that it only provides a one-dimensional measurement, so it may not capture the full complexity of a space or object. Additionally, factors such as obstructions or irregularities in the back wall may affect the accuracy of the measurement.

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