Speed of Sound. Introduction. Ryerson University - PCS 130

Transcription

1 Introduction Speed of Sound In many experiments, the speed of an object such as a ball dropping or a toy car down a track can be measured (albeit with some help from devices). In these instances, these objects are quite tangible and can be seen with the naked eye. Sound however is more elusive as it is hard for one to see but the speed can be similarly measured. Physically speaking, sound is a pressure wave propagated by the air particles. The wave propagates in the longitudinal direction (same direction as motion of travel of the wave) but is often visualized as a transverse wave (for easier representation). The speed at which that sound travels is given by the frequency of osciallation and wavelength: v = λf (1) If we know those two quantities, we could in fact determine the speed of sound. In this experiment, we can generate sounds of various single frequencies using things such as tuning forks, and tone generators. Determining wavelength can prove to be more challenging. However, if one were to create a system of standing waves, since the nodes of oscillation are fixed, we could relate the length of the tube system to the wavelength. Consider a tube with one end open and the other closed with length L. If standing waves were created such that at the open end, we get a loud volume (antinode) then we can deduce the wavelength as a function of length. As it turns out, many frequencies satisfy this condition for a closed ended tube of length L. The higher frequencies are typically referred to as the nth harmonic. f n = nv ; n = 1, 3, 5... (2) 4L Visual representation of standing waves in a closed ended tube Page 1 of 5

2 Speed of Sound setup Page 2 of 5

3 Apparatus Tone generator software (Audacity) Computer Adjustable closed ended tube system Tone generator (speaker) Water Thermometer Beaker Pre-Lab Questions Please complete the following questions prior to coming to lab. At the beginning of lab, you will be given a short quiz which is heavily based on one (or more) of these questions. 1.) Read through the entire lab writeup before beginning. 2.) From Eqn. 1, derive Eqn ) Describe how the first fundamental frequency changes when you change the length of an closed ended tube system. Write the general equation for length of an closed ended tube system as a function of frequency and harmonic number, n. 4.) In a closed ended tube system, describe where the nodes and anti-nodes are located when a standing (resonant) sound wave is formed. Try to describe this for the general case. 5.) Does the speed of sound increase or decrease with air temperature? In a few sentences explain why. Procedure 1.) Using a thermometer, record the ambient temperature of the room. 2.) Slowly fill the closed ended tube system with water making sure not to overfill the tube. The vertical position of the water reservoir dictates the water level in the plastic tube. The air volume above forms the closed ended tube system. 3.) Position the closed ended tube system at a comfortable height and connect the speaker to the headphone port of the computer. Make sure not to strain the wire. 4.) Make sure your computer s volume is set quite low. You can always increase the volume if the tone is too soft, but playing an extremely loud tone is unpleasant for everyone! Page 3 of 5

4 5.) Open the program Audacity which you can use to generate pure tones. To generate a tone, select Generate Tone. Leave the waveform as Sine, enter the frequency ( Hz is recommended), the amplitude (1 is recommended), and the duration (1 minute is recommended). Then click Generate Tone. 6.) Calculate the expected (theoretical) length at which you would expect the first harmonic to appear. 7.) Starting with a water level around where you would expect the first harmonic (in theory), click the green arrow in the audacity program to play the tone. 8.) Adjust the height of the water reservoir and determine the length at which the first resonance occurs. This is when you hear a volume maximum. 9.) Repeat the process again for four different frequencies. Analysis 1.) With the data obtained, plot tube length versus inverse frequency ( 1 f ). 2.) Find the value of the speed of sound v using a linear fit to your results. 3.) Use the relationship between the speed of sound in air v and the temperature T (expressed in Celsius) to determine a theoretical value of v: v = T (3) 4.) Find the percentage error of your v value from the value obtained above. 5.) What possible sources of error affected your results? Which one do you think had the largest effect. Wrap Up The following questions are designed to make sure that you understand the physics implications of the experiment and also to extend your knowledge of the physical concepts covered. Each member of your group should be able to answer any/all of these questions. Your TA will check that this is the case; please check out with your TA before exiting lab. 1.) With the frequencies you used, calculate the length needed for a few of the higher order harmonics. Using the experimental setup, see if you can hit a higher order harmonic - you might have to remove water from the apparatus to reach a low enough water level. 2.) What fundamental frequency would you need to generate for a closed ended tube of 13.5 cm? Calculate the frequency (using your speed of sound) and then verify it by generating a tone of that frequency and adjusting the tube length around 13.5 cm to ensure the max volume is indeed there. Page 4 of 5

5 Last Few Steps 1.) Save your data (in any format) with an easily identifiable name. 2.) Submit your data file to your group submission folder on D2L. 3.) Once this is complete and are certain that the data is saved, restart the computer when all experiments are completed. 4.) Tidy up your work station by ensuring the station is ready for your fellow students in other sections. Page 5 of 5