Physics - Measure Speed of Sound

Question

3) Suppose that the apparatus shown in the figure to the right is to be used to measure the speed of sound. The apparatus contains a tube that is open on both ends which has been placed into a beaker containing tap water. The distance between the top of the tube and the water level varies by raising or lowering the tube. Suppose that each lab group is provided with this apparatus as well as a ruler and tuning forks of various frequencies. By striking any particular tuning fork near the top of the tube, a standing wave may be created by adjusting the distance between the water level in the tube and the top of the tube.

(a) Design an experiment using the materials described above with the objective of measuring the speed of sound in air. Include steps to reduce uncertainty and include steps for describing your observations narratively and graphically.

(b) Consider the dependent variable(s) and independent variable(s) in your experiment. Make a sketch of the graph showing the general relationship between these variables and describe a method of graphical analysis that can be used to determine the speed of sound from the data.

(c) Suppose that two lab groups in different locations came up with different results. Other than measurement error, briefly describe two potential reasons for the differences.

Answer 1

(a) Experiment to measure the speed of sound using the apparatus described above:

1. Fill the beaker with tap water to a depth of about 5 cm.

2. Adjust the height of the tube so that the water level is about 1 cm below the top of the tube.

3. Strike a tuning fork with a known frequency near the top of the tube.

4. Slowly raise or lower the tube until a standing wave is created in the tube, with a node at the water level and an antinode at the top of the tube.

5. Measure the distance between the water level and the top of the tube.

6. Record the frequency of the tuning fork used.

7. Repeat steps 3-6 for several different tuning forks of known frequencies.

8. Calculate the wavelength of the sound wave using the equation λ = 2L/n, where L is the length of the tube and n is the number of nodes in the standing wave.

9. Plot the wavelength versus frequency on a graph.

10. Use the slope of the graph to calculate the speed of sound in air using the equation v = fλ.

To reduce uncertainty, several measurements should be taken for each tuning fork frequency and the average values should be used. The room temperature and humidity should be kept constant during the experiment as they can affect the speed of sound. The experiment should be conducted in a quiet room to avoid interference from external noise.

(b) The independent variable in this experiment is the frequency of the tuning fork, and the dependent variable is the wavelength of the sound wave. A graph of wavelength versus frequency can be plotted, with wavelength on the y-axis and frequency on the x-axis. The slope of the graph is equal to 2L, where L is the length of the tube, and the speed of sound can be calculated using the equation v = fλ.

(c) Two potential reasons for differences in results between lab groups in different locations could be differences in temperature and humidity, which can affect the speed of sound, and differences in the materials used to construct the apparatus, which could affect the length of the tube and the accuracy of the measurements.