Coke bottle on another planet, involving harmonics and speed

[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

 

[riseofphoenix]

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

 

[gneill]

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

 

[riseofphoenix]

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

n = 1, 3, 5, 7

So...

On Earth 2:

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

 

[riseofphoenix]

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

You still there?

 

[gneill]

You still there?

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

 

[riseofphoenix]

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

http://www.physicsclassroom.com/class/sound/u11l5d.cfm

^ That site says it's 1, 3, 5, 7

 

[gneill]

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

 

[riseofphoenix]

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

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

 

[gneill]

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

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

The second one is 520/3, right?

 

[riseofphoenix]

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

The second one is 520/3, right?

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?

 

[riseofphoenix]

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

The second one is 520/3, right?

Is 123.9 the answer to this problem?

 

[gneill]

Is 123.9 the answer to this problem?

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

 

[riseofphoenix]

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

I just did

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

 

[gneill]

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 canceled 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.

 

[riseofphoenix]

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 canceled 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.

What what??

You mean

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

 

[riseofphoenix]

I'm so confused now...

 

[gneill]

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

 

[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

 

[riseofphoenix]

Thanks!

 

[gneill]

Hmm. If L = 0.179m and f = 520 Hz for the harmonic n = 3 where n = 1, 3, 5, 7,... then

$v = \frac{4}{3}L f = 123.9 m/s$

 

[riseofphoenix]

Hmm. If L = 0.179m and f = 520 Hz for the harmonic n = 3 where n = 1, 3, 5, 7,... then

$v = \frac{4}{3}L f = 123.9 m/s$

Wait whattttt??

I already submitted it

Are you sure that's the answer?

I plugged in what you just wrote and got another answer.

v = (4/3)(0.179)(173.3)
v = 0.238666667(173.3)
v = 41.3?

If that's not correct and if you just plugged in f = 520 Hz, it gives a completely different answer (?)

v = (4/3)(0.179)(520)
v = 0.238666667(520)
v = 21507.68533?

What did you plug in??

 

[gneill]

On Earth 2:

For the second available harmonic, harmonics being 1, 3, 5, 7,...

$v = f \frac{4}{3}L$

Where f = 520 Hz, L = 0.179 m.

 

[riseofphoenix]

On Earth 2:

For the second available harmonic, harmonics being 1, 3, 5, 7,...

$v = f \frac{4}{3}L$

Where f = 520 Hz, L = 0.179 m.

-.-
kjbllajds... fudge.

ok.
thanks