# Tuning fork and resonances

## 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

Related Introductory Physics Homework Help News on Phys.org
diazona
Homework Helper
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?

for the first one, 56.5cm = lambda/4

the other resonance, 17.5 = 3lambda/4

is that right?

diazona
Homework Helper
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.

oh right...

first resonance: 56.5 + D = lamda/4

second resonance: 17.5 + D = 3lamda/4

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

How can that be?

diazona
Homework Helper
How do you know which resonance corresponds to which distance?

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

diazona
Homework Helper
Guesses are wrong sometimes, y'know

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?

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.