Resonance & Tubes: Frequency of Tuning Fork

[m.l.]

Homework Statement

An open vertical tube is filled with water and a tuning fork vibrates over its mouth. As the water level is lowered in th etube, resonance is heard when the water level has dropped 17 cm, and again after 49 cm of distance exists from the water to the top of the tube. What is the frequency of the tuning fork?

Homework Equations

lamda=2xlength, f=v/ lamda, speed of sound is 343m/s

The Attempt at a Solution

49-17=35

lamda=2l (or is it lamda=4l cause its a closed system?)
=2x.35
=0.70m

f=v/lamda
=343m/s/0.70m
= 4.9x10 exponent 2 Hz?

 

[LowlyPion]

1. Homework Statement
An open vertical tube is filled with water and a tuning fork vibrates over its mouth. As the water level is lowered in th etube, resonance is heard when the water level has dropped 17 cm, and again after 49 cm of distance exists from the water to the top of the tube. What is the frequency of the tuning fork?

lamda=2xlength, f=v/ lamda, speed of sound is 343m/s

3. The Attempt at a Solution
49-17=35

Isn't 49 - 17 = 32 ?

 

[nlightner]

I would like to clarify a few points before providing a response. First, is the tube open or closed? This information is important because it will affect the equation used to calculate the frequency of the tuning fork. If the tube is open, then the equation for calculating the frequency would be f = v/λ, where λ is equal to 2 times the length of the tube. If the tube is closed, then the equation would be f = v/λ, where λ is equal to 4 times the length of the tube.

Assuming the tube is open, the frequency of the tuning fork can be calculated using the given information. The distance between the water level and the top of the tube is equal to 49 cm - 17 cm = 32 cm = 0.32 m. Plugging this value into the equation for λ, we get:

λ = 2(0.32 m) = 0.64 m

Now, using the speed of sound in air (343 m/s), we can calculate the frequency of the tuning fork:

f = 343 m/s / 0.64 m = 535.9 Hz

Therefore, the frequency of the tuning fork is approximately 535.9 Hz. It is important to note that this value may not be exact due to rounding and possible experimental error.