# Transverse waves on string

1. Feb 27, 2015

### Emily_20

1. The problem statement, all variables and given/known data
A new musical instrument is fashioned from a metal can of length L and diameter L/10, open at one end, with a string stretched across the diameter of the open end. The string is tensioned such that the 3rd harmonic frequency of the vibrating string matches the fundamental frequency of the can.

a) What is the mathematical relationship between the speed vt of transverse waves on the string and the speed va of longitudinal waves in the can?

b) What happens to the sound produced by the instrument if the tension in the string is doubled? Describe what happens to both the pitch and the intensity, and defend your answer with an argument as quantitative.

2. Relevant equations
Fn = nv/4L, v=f *lambda

3. The attempt at a solution
a) 3v/4L=1v/4L
Fcan= Fstring

b) The frequency goes up.

I need help with these two questions.

2. Feb 27, 2015

### Simon Bridge

... You have just written that 3=1 (multiply both sides by 4L/v) - this is false.

The frequency formula you have written above does not work for both can and string.
You need to distinguish between the speed values for the can and the string.

If you sketch the wave-form, instead of relying on picking the right equation, you should be able to relate the lengths in question to the wavelengths of the waves.
The equation you want is $v=f\lambda$

3. Feb 27, 2015

### Emily_20

The problem is that I do not even know how to sketch the wave-form. I do not even think that I understand what's the point of this problem.. maybe thats why I cannot solve it...

4. Feb 27, 2015

### Emily_20

Here is an attempt for a sketch but I am not sure if its right..

5. Feb 27, 2015

### Simon Bridge

Good - you got the wave-form on the string - now you can write out the wavelength in terms of L.
Notice that one wavelength fits 2/3rds of the string...

On the same diagram, you can sketch in the pressure wave for the can.

The point of the problem is to exercise your understanding. You get a lot of these puzzle-type things before you can be turned loose on a real example.

Last edited: Feb 27, 2015
6. Feb 28, 2015

### Emily_20

Hello sir, thank you for your help I appreciate it.
I wrote out the wavelength in terms of L for both can and string and I tried to write the mathematical relationship using it, is that correct?

Last edited: Feb 28, 2015
7. Feb 28, 2015

### Emily_20

I think I made a mistake in the calculation in Vt/L = 3/2 Va/ L/15

Last edited: Feb 28, 2015
8. Feb 28, 2015

### BvU

In your original equation you had a 4. Now you have L = $\lambda_c$.
What is the wavelength that matches the fundamental frequency of the can ?

9. Feb 28, 2015

### Emily_20

I'm not even sure if my original equation is correct. I though at the beginning that the string will act with a frequency for a tube with one open end and one closed end thats why I had a 4. For the wavelength of the can I used L=λc

10. Feb 28, 2015

### BvU

Well, to me the description and your drawing look a lot like "a tube with one open end and one closed end" !

11. Feb 28, 2015

### Emily_20

Thanks for the help I appreciate it. If I understand its right so the can is actually going to have a frequency of Fn = nv/4L and the string is going to have a frequency of f=V/λ

12. Feb 28, 2015

### BvU

Do distinguish $\lambda_{string} = {2\over 3} \; {L\over 10}$ and $\lambda_{can} =$ ...
And: do distinguish $v_{string}$ and $v_{can}$.
What is equal is the tone, i.e. the ...

13. Feb 28, 2015

### Emily_20

4L? because the can has a frequency of f1 and the string is going to have a frequency of f3

Last edited: Feb 28, 2015
14. Feb 28, 2015

### Emily_20

Simon Bridge said that I can sketch in the pressure wave for the can what does he mean by pressure wave?

15. Feb 28, 2015

### Simon Bridge

If you prefer, sketch the logitudinal wave along the can.
The wave in the can is a sound wave in air... i.e. a wave of variations in air pressure.
You have notes that show the harmonics in a tube that is open at one end.

You can reason it out ... in the logitudinal wave, the air particles move the most at antinodes, and the least at nodes, where do those have to be? You are also told that the wave is the fundamental.

This way of reasoning through the physics is more reliable than trying to remember the right equation.

16. Feb 28, 2015

### Emily_20

I got that the wavelength of the string is 2/3 (L/10) and the wavelength of the can is 4L is that correct?

17. Feb 28, 2015

### Simon Bridge

Some notes... when you wrote. $$\lambda_s =\frac{2}{3}L=\frac{2}{3} \frac{L}{10}$$... that was nonsense. Can you see why?

You keep making that kind of mistake... it will cost you marks.
It is very important that you figure it out.

18. Feb 28, 2015

### Emily_20

Unfortunately, I am very confused. Physics is not my strength. This problem is very important for me

19. Feb 28, 2015

### Simon Bridge

Can you explain how those should be correct? Reasoning is more important than being right.
The point of getting you to sketch things out is so you wont need to ask if its correct, there will only be one possibility.

20. Feb 28, 2015

### Emily_20

I thought the the wavelength of the string is the diameter of the can. If the string has a 3rd harmonic frequency and its an open pipe I though using the equation λs=2/3L. For L I used the diameter of the can because its the length.