A 42.9cm long tube has a 42.9cm long insert that can be pulled in and

[cmkc109]

Homework Statement

A 42.9cm long tube has a 42.9cm long insert that can be pulled in and out. A vibrating tuning fork is held next to the tube. As the insert is slowly pulled out, the sound from the tuning fork creates standing waves in the tube when the total length L is 46.8cm, 79.2cm, and 111.6cm. What is the frequency of the tuning fork? Take the speed of sound in air to be 343m/s

Homework Equations

open-closed end
(2n-1)/ 4 lamda = L

The Attempt at a Solution

so I know this question has been posted before, but I don't really understand the solution.
79.2 - 46.8 = 32.4 cm or 0.324m

Why do you need to multiply 0.324 by 2 to get the wavelength?

Since it is open-closed, isn't it 1/4 lamda = L , which is times it by 4?

 

[jldibble]

A standing wave is an effect of constructive/deconstructive interference as the wave enters the tube, reflects, and crosses paths with itself. In this case, the differences between these measurements are the distances from antinode to antinode. And as we know, the distance from antinode to antinode is one half the wavelength. This is why you must double the distances to get the wavelength.

79.2-46.8 = 32.4
111.6-79.2 = 32.4

32.4 cm = distance from antinode to antinode.

2*(distance from antinode to antinode) = wavelength


Hope this helps

 

[cmkc109]

sorry I don't really understand constructive and destructive interference..
all i know for destructive is that it is 1/2 a integer, constructive is something about whole numbers...
and how do u know it is from antinode to antinode?

 

[jldibble]

I suppose the problem doesn't require you to understand why a standing wave is formed...it seems like it should have come up though before.

Anyway, refer to this site. It words it a bit better than i could.

http://hep.physics.indiana.edu/~rickv/Standing_Sound_Waves.html

 

[cmkc109]

ok thanks!

 

[cmkc109]

your site actually gives quite different information from what my notes said.
My notes said in the open end, you will get antinode, but the site said it opposite..

 

[haruspex]

your site actually gives quite different information from what my notes said.
My notes said in the open end, you will get antinode, but the site said it opposite..

A problem with discussing sound waves in pipes is that you can think of the wave in terms of displacement or in terms of pressure. AFAIK, it's most common to use displacement. In that case, there is zero displacement at the closed end and maximum at the open end. A node always refers to where the amplitude is a minimum, so in this view the node would be at the closed end.
The site jdibble links discusses the wave in terms of pressure. The pressure changes most where the displacement is least, and v.v. So now the node is at the open end, etc.
In principle, the same confusion could arise with waves in strings, etc., but I'm not aware that it ever does.

 

[cmkc109]

ok thanks haruspex
so my notes express waves in terms of dispalcement
in the website, it express waves in terms of pressure
is that correct?

 

[haruspex]

Yes.