# Coke bottle on another planet, involving harmonics and speed

1. Dec 1, 2012

### riseofphoenix

This is what I tried doing, but I ended up getting an answer that isn't listed above

1. frequency = speed/wavelength

2. On Earth

480 Hz = (343 m/s)/wavelength
wavelength = 343 / 480
wavelength = 0.714 is the wavelength for the Coke bottle

3. On Earth 2

Since they already gave me frequency on Earth 2, and I already solved for wavelength, all I have to do is plug in those numbers to solve for speed on Earth 2.

frequency = speed/wavelength
(520 Hz) = speed/0.714
(0.714)(520) = speed
371.58 m/s = speed

2. Dec 1, 2012

### riseofphoenix

Wait...I think first i have to find the harmonics...

3. Dec 1, 2012

### Staff: Mentor

You're dealing with a fundamental frequency on Earth, but a harmonic on Earth 2. What harmonics can a closed-bottom cylinder produce?

4. Dec 1, 2012

### riseofphoenix

n = 1, 3, 5, 7

So...

On Earth 2:

520 = 5*104 (fifth harmonic of 104 Hz)

5. Dec 1, 2012

### riseofphoenix

You still there?

6. Dec 1, 2012

### Staff: Mentor

Still here. You should confirm which harmonics can be produced by a closed-end pipe.

7. Dec 1, 2012

8. Dec 1, 2012

### Staff: Mentor

So, when the problem states that "a second available harmonic of 520Hz is available", which one do you think they're referring to?

9. Dec 1, 2012

### riseofphoenix

312/3 = 3*104 (second available harmonic of 104)
520/5 = 5*104 (third available harmonic of 104)

10. Dec 1, 2012

### Staff: Mentor

Why 104? The frequencies will go: 520, 520/3, 520/5, 520/7,...

The second one is 520/3, right?

11. Dec 1, 2012

### riseofphoenix

Ohh!

that's right, because I was thinking the whole time the the numbers HAD to be integers...

Yeah that's what I meant to say!

But what next though?

Do I then do:

1. frequency = speed/wavelength

2. On Earth

480 Hz = (343 m/s)/wavelength
wavelength = 343 / 480
wavelength = 0.714 is the wavelength for the Coke bottle

3. On Earth 2

Since they already gave me frequency on Earth 2, and I already solved for wavelength, all I have to do is plug in those numbers to solve for speed on Earth 2.

frequency = speed/wavelength
(173.3 Hz) = speed/0.714
(0.714)(173.3) = speed
123.76 m/s = speed?

Last edited: Dec 1, 2012
12. Dec 1, 2012

### riseofphoenix

Is 123.9 the answer to this problem?

13. Dec 1, 2012

### Staff: Mentor

You'll have to show your work; I can't verify a guess

14. Dec 1, 2012

### riseofphoenix

I just did

frequency = speed/wavelength
(173.3 Hz) = speed/0.714
(0.714)(173.3) = speed
123.76 m/s = speed

15. Dec 1, 2012

### Staff: Mentor

I have a problem with the length of column (bottle) that you're using (Think about a coke bottle over 70cm tall!). While the error has fortunately cancelled out along the way, I can't in good conscience say that your answer is altogether correct

On the web page that you found, take a look at the table partway through that shows the column length \ wavelength relationship for the various harmonics. Note that the fundamental is NOT the same length as the column.

16. Dec 1, 2012

### riseofphoenix

What what??

You mean

Wavelength = (4/3)*L
Wavelength = (4/3)*(0.714)
Wavelength = 0.952????

17. Dec 1, 2012

### riseofphoenix

I'm so confused now...

18. Dec 1, 2012

### Staff: Mentor

On Earth 1, the fundamental is 480Hz, speed 343m/s. Wavelength is then 0.715m. That's fine. But the bottle has length L = λ/4, so L = 0.179m. The length is assumed not to vary between planets (same bottle).

So take that bottle length and the harmonic 520Hz and use the appropriate length versus wavelength relationship to find the speed (since v/f = λ, and λ = (4/3)L for this harmonic).

Sorry, gotta go now to an important meeting with a pint of something refreshing

19. Dec 1, 2012

### riseofphoenix

Earth 1

Step 1) Find wavelength
Fundamental frequency on Earth 1: 480 Hz
Speed on Earth 1: 343 m/s.
Wavelength on Earth 1: λ = v/f, which is 343/480 = 0.715 m

Step 2) Find the length of the bottle
The bottle has length L = λ/4
L = (0.715 m)/4
L = 0.179 m

The length is assumed not to vary between planets (same bottle).

Earth 2

Step 3)
Take that bottle length (L = 0.179) and find the second available harmonic of 520 Hz.

Since the bottle is a close-ended cylinder, n = 1, 3, 5, 7 and the frequencies will go: 520, 520/3, 520/5, 520/7. The second available harmonic of 520 Hz is 520/3 = 173.3
According to: http://www.physicsclassroom.com/class/sound/u11l5d.cfm

Step 4) To find speed, use v = λf (speed = wavelength*frequency). λ for the second available harmonic of 520 Hz will = (4/3)L

λ = (4/3)(0.179)
λ = 0.239

So,

v = λf
v = (0.239)(173.3)
v = 41.3 m/s

20. Dec 1, 2012

Thanks!