How Do You Calculate the Frequency of a Tuning Fork Using Water Resonance?

[mizzy]

Homework Statement

A tuning fork is held over the top of a graduated cylinder that is slowly filled with water. Resonances are noted when the water level is 56.5cm and 17.5cm below the rim. Note that there is an end correction , meaning that the effective length of the air column is longer than the observed length by a fixed constant amount. If the speed of sound is 343m/s, then find the frequency of the tuning fork.

Homework Equations

f = v/lambda

1st resonance = lambda/4

2nd resonance = 3lambda/4

The Attempt at a Solution

I drew the cylinders. One cylinder is 56.5 cm below the rim and the other is 17.5cm below the rim. The first cylinder is at the second resonance of 3lambda/4 and the second is lamda/4. Now i don't know what to do. Can someone guide me?

thanks

 

[diazona]

Consider the resonances one at a time. For example, the first one, which is 56.5 cm below the rim, and is at 3λ/4. What is the relationship between those two distances?

What about the other resonance?

 

[mizzy]

for the first one, 56.5cm = lambda/4

the other resonance, 17.5 = 3lambda/4

is that right?

 

[diazona]

Note that there is an end correction , meaning that the effective length of the air column is longer than the observed length by a fixed constant amount.

I don't believe you've taken this piece of information into account.

 

[mizzy]

oh right...

first resonance: 56.5 + D = lamda/4

second resonance: 17.5 + D = 3lamda/4

 

[mizzy]

k. I solved these equations, but I get a negative wavelength and therefore a negative frequency.

How can that be?

 

[diazona]

How do you know which resonance corresponds to which distance?

 

[mizzy]

i don't know. I'm just guessing the the first would be the second and the second distance is the first.

 

[diazona]

Guesses are wrong sometimes, y'know

 

[mizzy]

k. let me think about this one. We are dealing with a tube that is open on one end and closed in the other. Equations i know to use for this situation: lambda = 4L , f = n(v/4L) when n= 1,3,5,etc.

In the question, the tube is slowly filled with water and the resonances are noted at the distances above..the first resonance happens at 56.5cm.

am i going in the right direction?

 

[mizzy]

K. I tried drawing a picture so i can visualize this. The second resonance will happen at 56.5cm and the first resonance will happen at 17.5cm.

I got the answer.