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

[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

 

[PeterO]

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?

 

[jamcintyre1]

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.

 

[PeterO]

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?

 

[Nickie]

is the correct answer.

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.