IntroductionTheoryProcedureThe Speed of Sound in AirThe Speed of Sound in Some Other MaterialConclusionsSpeed of SoundI b elieve the use of noise to make music will increase until we reach a music producedthrough the aid of electrical instruments which will make available for musical purposesany and all sounds that can be heard.comp oser John Cage, 19371 IntroductionThere are many ways to determine the speed of sound. The method we will use in this lab is both fairlystraight forward and the equipment needed is fairly minimal. We will be creating sounds and recordingthem with two microphones. We will measure the difference in distance between the paths the sounds takefrom going to the two microphones. We will then study the recorded signals of the sound to see the timedifference between how long the sound took to get to each microphone. Our measurement of the speed ofsound will be the result of dividing the difference in distance by the difference in time.1.1 TheorySound is a vibrational wave that travels through a medium. The speed of sound in a medium depends onhow quickly the energy of the vibration can be transferred across the medium. While the details of theequations that are used to find the speed of sound will vary depending on the state of the medium, thebasic equation∂2u∂t2= c2∇2u (1)describes the wave where u describes the medium the wave is moving through, and c is the speed of thewave [Hecht and Zajac, 1987].In a sound wave, the general method to find the speed is fromvs=s∂p∂ρ(2)where p is the pressure and ρ is the mass density [Landau and Lifshitz , 1993]. In fluids, the speed can berecast in terms of the bulk modulus, B,vs=sBρ(3)which describes the change in volume undergone by a medium when the pressure changes [Halliday et al.,2001]. Similarly, in a solid the sound speed depends on the Young’s modulus, Y ,vs=sYρ(4)which describes the stress divided by the strain.1For gases, the bulk modulus is not always easy deal with, since it will in general vary with temperature,pressure, and density. So the speed of sound equation is often recast using the terms of ideal gases:vs=rγkTm(5)where γ is adiabatic index (which is equivalent to the specific heat at constant pressure divided by thespecific heat at constant volume), k is Boltzmann’s constant, T is the temperature and m is the molecularmass [Landau and Lifshitz, 1993]. For dry air we will take γ = 1.4 and m = 28.9645 u. Unfortunately, airis not a perfectly ideal gas, so to determine the speed of sound more exactly pressure and humidity mustbe considered. Consideration of these effects does not lead to simple equations, though, so in practicetables or numerical approximations are typically used.2 Procedure2.1 The Speed of Sound in AirIn this lab we will be using the program audacity on a Linux computer to record sounds received bytwo microphones. Using the provided adapters you will save one microphones sound as the left track ofa stereo recording and one as the right track. For all of the measurements that you make below, be sureto establish reasonable uncertainties and to make notes in your lab notebook about why you picked theuncertainties that you used.Record the air temperature, pressure and humidity for the time of your measurements. Currently wehave 1 device that will make all three measurements.Your first order of business is to figure out how you need to use the provided adapters and cords tohook up the microphones to the computer. Once you believe that you have the cords set up right, open upaudacity and configure that program to receive stereo input. Then test each microphone separately, to besure that they are providing signals to the correct channel. Once you are convinced that each microphoneis working correctly, try both microphones at the same time. Play with causing a sound closer to onemicrophone or the other and see if your recorded signals make sense.Once you are convinced that your setup is correctly recording the signals to both microphones, takeseveral sets of data that you can use to find the speed of sound. Remember that the distance that will gointo your calculations is the difference in the path length traveled by the sound to each microphone.For the time difference between how long it takes the sounds to get to each microphone, first useaudacity directly. Zoom in on your recordings, pick notable locations in the sound waves, and read offthe time difference between when those portions of the wave appear in the left and the right channels. Besure to assign an uncertainty to the time difference. Be sure to print off at least one set of sample signalsfrom audacity and use the plots when explaining your method. You may need to create a screenshot inorder to extract plots from audacity.Repeat this process for at least five different path length differences for the sound’s travel to the twomicrophones. Be sure to have your path difference use the entire range of possible values allowed by thesupplied equipment. Plot your results as path length difference versus time delay and fit the line to finda value for the speed of sound in air.2.2 The Speed of Sound in Some Other MaterialIn this section of the lab you are in charge. Use the techniques that you learned in the previous section tofind the speed of sound in some material other than air. In your lab notebook describe in detail what youdo on this portion. Note that you should be very careful to condsider the fact that the sound may travelboth through the material that you are attempting to test and the air.23 Conclusions1. Find online or in a book a source for the speed of sound in air that considers temperature, humidity,and pressure. This source may have equations, tables, or web forms that give the speed of sound.Cite your source. Find the speed of sound using equation 5 and your source and compare. Also,try slightly varying the temperature, pressure, and humidity that you use and see how the resultschange. Variations in which parameters make the most difference here? Why? Use these values tocome up with a theoretical value of the speed of sound in air with uncertainty for the time of yourmeasurements. Explain how you decided on your value.2. How do your results for the speed of sound in air compare to the published values? Are the valuesconsistent to within their uncertainties?3. What is the published value for the speed of sound in the other material that you tested and whatis your source for the speed? How do your