Resonance - Tuning fork volume

[Clean]

[SOLVED] Resonance - Tuning fork volume

Homework Statement

A narrow plastic pipe is almost completely submerged in a graduated cylinder full of water, and a tuning fork is held over its open end. The pipe is slowly raised from the water/ An increase in loudness of the sound is heard when the pipe has been raised 17 cm and again when it has been raised 51 cm.

If the pipe continues to be raised, how far from the top of the pipe will the water level be when the next increase is loudness is heard?

Homework Equations

L = 5(wavelength)/4

The Attempt at a Solution

L = 5(wavelength)/4
L = 5(68 cm)/4
L = 85 cm

Thanks!

 

[anathema]

I would like to provide a more detailed explanation of the phenomenon observed in this experiment. The increase in loudness of the sound when the pipe is raised from the water is due to a phenomenon called resonance. Resonance occurs when a vibrating object, such as the tuning fork, causes another object, in this case the air column in the pipe, to vibrate at its natural frequency.

In this experiment, the length of the air column changes as the pipe is raised from the water. The first increase in loudness occurs when the length of the air column is equal to one-quarter of the wavelength of the sound produced by the tuning fork. This can be calculated using the formula L = 5(wavelength)/4, where L is the length of the air column and wavelength is the distance between two consecutive compressions or rarefactions in the sound wave.

Using the given information, we can solve for the wavelength of the sound produced by the tuning fork:
L = 5(wavelength)/4
17 cm = 5(wavelength)/4
wavelength = (17 cm * 4)/5 = 13.6 cm

Therefore, the wavelength of the sound produced by the tuning fork is 13.6 cm. This means that when the pipe is raised 17 cm from the water, the length of the air column is equal to one-quarter of the wavelength and resonance occurs, resulting in an increase in loudness.

The second increase in loudness occurs when the length of the air column is equal to three-quarters of the wavelength. This can be calculated by adding one wavelength to the length of the air column calculated in the first step:
L = 5(wavelength)/4
51 cm = 5(wavelength)/4
wavelength = (51 cm * 4)/5 = 40.8 cm

Therefore, when the pipe is raised 51 cm from the water, the length of the air column is equal to three-quarters of the wavelength and resonance occurs again.

To find the next point at which an increase in loudness will occur, we need to add one more wavelength to the length of the air column calculated in the second step:
L = 5(wavelength)/4
wavelength = (40.8 cm + 40.8 cm) = 81.6 cm

This means that when the pipe is raised 81.6 cm from the water, the length of the air column will be