Year 12 Sound Problem (Involves resonance in a closed pipe).

[caitie_72]

Homework Statement

Hi :)
This question is from a test i had today. For some stupid reason we get to finish it off tomorrow. I figured i do what everyone else will, and sort out the what i didn't understand. Luckily this was it. Anyway, the question is typed from memory so it may seem a bit odd or inaccurate.

A pipe is in a tub of water. As it is moved down (or up, can't remember!) it resonates at 288 Hz and 512 Hz. The distance between these two points is 13.9 cm (0.139 m). What is the velocity of sound in the tube?

I'm not sure of the order of frequencies occurring is. I think it was probably the lowest frequency first. I don't really need an answer, just an understanding of how to do a problem like this. All i know is that the pipe resonates at those two frequencies, and the distance between the points where it resonates is 13.9m. If you've ever seen a question like this ... then you'd probably get what i mean, hopefully.
Do I used simultaneous questions? I'm not sure.

Homework Equations

(w=wavelength)
v=F*w

The Attempt at a Solution

What i did first, in a fit of irrational confusion, was find the wavelength. I assumed that resonance was occurring at either nodes or antinodes, half a wavelength apart (?)
So w = 2 * 13.9.

Then i got confused, because i know the fundamental wavelength of a closed pipe is w=4L.

Then i did something stupid i knew wasn't right. Found the difference between the frequencies and then multiplied it with the wavelength. Stupid stupid, i know. Makes no sense.

I'm thinking simultaneous equations?
f=v/4L.

512=3v/4L 288=v/4L

Resonance must be occurring at first and second modes, right?
I'm just confused about what the length is! Does length, in this case, mean the length of the whole pipe or the length between the points of resonance? Does resonance occur at half wavelengths or quarter wavelengths? Don't understand!

Any help or direction at ALL is appreciated. Thanks :)

 

[rl.bhat]

Since there is no other information, you have to assume that they are resonating in the fundamental mode.
So write 512=3v/4L 288=v/4L as 512=v/4L1,and 288=v/4L2. Write these equation in terms of L1 and L2. L1 - L2 is given. Solve for v.

 

[caitie_72]

Thank you so much! You are seriously my favourite person ever right now.
Just checking, am i doing it right?

L1=3v/2048
L2=v/1152

0.139 = 3v/2048 - v/1152
v = 232.9 m/s

I assume so. Thanks again :)

 

[rl.bhat]

L1=3v/2048
This is wrong. It should be L1=v/2048. Find L2-L1.