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Synopsis¶

This lab will follow a similar overall flow as the transverse waves lab (the one with the tuning forks and strings). In this case, we will be looking at longitudinal waves, in the form of sound.

Effectively, given a tuning fork of a particular frequency, we will be increasing and decreasing the length of a tube of error to create standing sound waves in the tube. This will allow for the determination of the wavelength of the waves, which then allows for determining the speed of sound.

In the transverse waves lab, the speed of the waves was determined by the tension in the string, which could be modified by changing the weight attached to the string. In this case, the speed of the sound waves is determined by air density, temperature, humidity, none of which are easily controllable without doing fancy/unpleasant things (turning up the room temperature significantly, etc.). Thus, in this case, the sound speed is a fixed quantity we will measure and compare to the expected value.

Theory¶

For this lab, you have a tube partially filled with water. The water level in the glass tube can be raised or lowered by raising or lowering the metal vessel. When a tuning fork is places at the opening of the tube, sound waves travel down the tube and bounce off the water, and then travel back up the tube. If the length of the air tube is modified, a standing wave can be formed. In order to form a standing wave, it is necessary that the length of the tube satisfies $L=n\lambda/4$ , with n=1,3,5,7,...

The reason for this is that the water-end of the air tube needs to be a node, and the air-end of the tube needs to be an antinode, as shown below. Recall that one wavelength begins at an antinode, continues through the next antinode, and ends at the antinode after that (i.e. the distance between two antinodes is half the wavelength), such that the diagrams below show the pressure wave structure for n=1, 3, and 5, respectively.

Airtube

Figure 1: Schematic diagram of pressure waves in the tube.

Velocity can be determined using the formula $v=f\lambda$ , and each fork is labeled with its frequency. Thus, measuring the wavelength allows for measuring the speed of sound.

Finally, the speed of sound is approximately $331.36\frac{m}{s}\sqrt{\frac{T}{273}}$ , where T is the temperature in Kelvin.

Procedure¶

Take a tuning fork with a frequency greater than 256 Hz.
Fill the reservoir with water, such that the water level is high.
Change the water level to find the point where the sound is loudest (the fundamental resonance).
Determine the tube length for two successive resonances.

Repeat the process for another tuning fork (of a different frequency)

Repeat the process for a third tuning fork (of a different frequency)

Based on the relation between wavelength and tube length, $\lambda=2|L1-L2|$ if L1 and L2 are the tube lengths for subsequent resonances. Using this formula, calculate the wavelength for each fork.

Using the relation between wavelength, frequency, and speed, calculate the speed of sound for each fork. Extra credit! Can you idenfity the location of additional harmonics? Record them below for a single frequency (or a single fork) - Give answers here (including uncertainties; assume the uncertainty on f is 0 for simplicity but propagate the uncertainties on L1 and L2 to wavelength and then to v). First fork: f= L1= L2= $\lambda$ = v=

Second fork: f= L1= L2= $\lambda$ = v=

Third fork: f= L1= L2= $\lambda$ = v= Determine the temperature with a thermometer to calculate the expected sound speed. Are your measurements consistent with the expectation? - Give answer here

Based on the error in the temperature measurement, propagate the uncertainty to the measurement of the speed of sound Do you think increasing the diameter of the tube would increase or decrease the measured speed?
Give answer here