# Finding the Location of the 2nd Antinode in a Standing Wave at 4.10 Meters

• jamcintyre1
In summary, the conversation discusses the location of the 2nd antinode in a standing wave, with the 4th node occurring at a position of 4.10 meters. The equation for nodes and antinodes is mentioned, but the correct location for the 2nd antinode cannot be determined without further information. The possibility of the standing wave being on a string, in an open pipe, or in a stopped pipe is also brought up.
jamcintyre1

## Homework Statement

The 4th node of a standing wave occurs at a position of 4.10 meters. Where is the 2nd antinode?

## Homework Equations

nodes occur at: x=n*(λ/2)
antinodes: x=(n+.5)*(λ/2)

## The Attempt at a Solution

n=4??
4.1m=2λ→λ=2.05m
now n=2? x=(2+.5)*(λ/2)≈2.56m wrong!
x=1.54m

jamcintyre1 said:

## Homework Statement

The 4th node of a standing wave occurs at a position of 4.10 meters. Where is the 2nd antinode?

## Homework Equations

nodes occur at: x=n*(λ/2)
antinodes: x=(n+.5)*(λ/2)

## The Attempt at a Solution

n=4??
4.1m=2λ→λ=2.05m
now n=2? x=(2+.5)*(λ/2)≈2.56m wrong!
x=1.54m

No answer to that question as it stands.

Was there any particular feature of the standing wave at position 0.00 metres?

I didn't get any more info. the solution has a sin graph I think with the 2nd antinode as the 2nd max which mazes sense, so 1.5*wavelength/2. But I can't figure out why the equation won't work. Thanks for your help btw. I'll take a look at you question.

jamcintyre1 said:
I didn't get any more info. the solution has a sin graph I think with the 2nd antinode as the 2nd max which mazes sense, so 1.5*wavelength/2. But I can't figure out why the equation won't work. Thanks for your help btw. I'll take a look at you question.

This standing wave ..

Is it on a string, fixed at one end at 0.00

Is the standing wave in an open pipe? An open pipe that runs form 0.00m to some distant point?

Is this standing wave in a stopped pipe? A stopped pipe with its stopped end at 0.00?

I would like to add that the formula for finding the location of an antinode in a standing wave is x=(n+.5)*(λ/2), where n is the number of the antinode. In this case, n=2, so the location of the 2nd antinode would be x=(2+.5)*(λ/2)=1.5*(2.05m/2)=1.54m. It is important to note that in a standing wave, the distance between two consecutive nodes or antinodes is always equal to half the wavelength. Therefore, by using the given information of the 4th node occurring at 4.10 meters, we can calculate the wavelength and then determine the location of the 2nd antinode. This is a fundamental concept in understanding standing waves and their properties.

## What are standing waves?

Standing waves are a type of wave that occurs when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other. This creates a pattern of nodes (points of no movement) and antinodes (points of maximum movement) that appear to be standing still.

## What causes standing waves?

Standing waves are caused by the interference of two or more waves with the same frequency and amplitude traveling in opposite directions. This interference can occur in any medium, such as air, water, or a solid object.

## What are some examples of standing waves?

Some common examples of standing waves include vibrations on a guitar string, sound waves in a pipe or organ, and electromagnetic waves in an antenna. Standing waves can also occur in natural phenomena, such as ocean waves bouncing off a cliff.

## What are the characteristics of standing waves?

Standing waves have several characteristics, including a fixed frequency, nodes and antinodes that do not move, and a standing wave pattern with points of maximum and minimum amplitude. The number of nodes and antinodes in a standing wave depends on the wavelength and the boundaries of the medium.

## How are standing waves used in technology?

Standing waves have many practical applications in technology, such as in musical instruments, microwave ovens, and medical imaging devices. In musical instruments, standing waves in strings or pipes produce specific frequencies and pitches. In microwave ovens, standing waves are used to evenly heat food. In medical imaging, standing waves are used to create images of the body's internal structures.

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