Laboratory 3 Seth M. Foreman February 24, 2015 Waveforms and the Speed of Sound 1 Objectives The objectives of this excercise are: to measure the speed of sound in air to record and analyze waveforms of simple tones 2 Introduction At room temperature and standard atmospheric pressure, sound travels at approximately 343 meters per second. Electronic measurement is now fast enough that we can resolve the very small amount of time that passes as sound moves back and forth in a laboratory environment (on the order of just a few milliseconds). To compute an experimental value for the speed of sound, you will actually use a simple relation: distance covered divided by elapsed time is equal to speed. In this experiment, we will make sound travel along a cardboard tube of length L. As the sound travels down and then back the tube, the total distance traveled will be 2L. If this happens in a time interval that we call t, we then have v s = 2L t (2.1) (Note: in physics, we normally use the greek letter to represent an interval or a difference. Thus, t usually refers to a time interval, while x usually refers to a difference in position.) The trick now is to find a reliable value for the elapsed time, which is essentially impossible to measure manually. (Unless you have the reflexes and hearing of a bat!) We will make a sharp noise at one end of a long cardboard tube, and somehow measure the time it takes for that sound to move to the opposite end of the tube, reflect, and move back to the initial end. By using a sensitive sound sensor (microphone) at one end of the tube, we hope to detect both the moment the sharp sound is made and also the moment this sound pulse returns to the microphone after being reflected from the other end. We will use a microphone that can collect 5, 000 or more measurements each second (we say it has a sampling rate of 5, 000 Hz or more ). Thus, we will 1
be able to plot the output from the microphone with 5 points measured per millisecond. Since we expect the time t to be of the order of 10 milliseconds, we should then have enough points to make a good graph from which to extract our results. For a tube closed on one end, sound will obviously reflect. Remarkably, sound will even reflect from the end of a fully open tube! The abrupt change from the confines of the tube to the open air of the room creates a certain boundary for the sound pulse. While most of its energy exits the tube, some of its energy is reflected back to the origin of the sound (this is the principle behind open organ pipes). 3 Procedure We will use a sound detector in conjunction with the software package and computer interface. The microphone and interface translate pressure differences in sound waves to voltage differences that you can plot in a voltage-versus-time graph. You dont actually have to worry about what you are plotting exactly. All that is important is to see how the signal evolves in time, since all you need is a time measurement. The only timing problem for our laboratory set-up occurs because the computer cannot plot data as fast as it receives data. When you start collecting data from the sound sensor, wait until the data appears on the screen before hitting the STOP button. 3.1 Determining the speed of sound v s Measure and record the length L of the cardboard tube. Make sure your sound sensor is set to a sampling rate of at least 5, 000 Hz through the computers user interface. You can find the required menu by double-clicking on the icon of the sound sensor. Make sure you are plotting sensor voltage versus time on the computer. Situate the sound sensor at one end of the tube, and select a noisemaker. Practice making a single clear click or pop sound, and hold this noisemaker near the sound sensor. Hit the start button and immediately make a single clear click or pop noise. Examine the plot of voltage-versus-time. Zoom-in to see the sharp voltage signal in detail. A sharp peak should appear where the sound was made, and some time later, another smaller signal appears. The time difference you measure here between the main large peak and the main secondary peak is t, the time elapsed while sound traveled back and forth in the tube. Take five separate measurements of t and compute the speed of sound in each case. Average them and report this average as your result for t. Use your reported result in Eqn. 2.1 to compute v s. Does your value agree closely with the accepted value of 343 m/s? Include at least one printout of a plot of sensor-voltage versus time with your report. 3.2 Recording waveforms Set the sampling rate to 10, 000 Hz for the sound sensor. Strike the tuning fork provided and start recording the sound of the tuning fork until waveform data appears on the voltage-versus-time graph. 2
Enlarge the waveform until you can see the sinusoidal variations. Send this graph to the printer. Using this graph, measure the period of the sound wave. Find and report the frequency f by finding the reciprocal of the period. Does it match the frequency printed on the tuning fork? Try to simulate the tuning forks tone with your voice and record this sound. What does the waveform look like now? Describe it in detail. Can you see more than one frequency at work? Now record a brief (about one second long) sound of your choosing hopefully you remembered to bring an interesting sound to lab today! If you didn t, try saying a one-syllable word into the sound sensor. Plot the result. This waveform is made of many sinusoidal waves of differing frequency and amplitude (you will learn about this process of Fourier analysis from the lectures...). Many speech recognition systems work with signals just like this one. Each persons voice will look a little different in these plots, and each word has a distinct waveform signature. Include one printout each for the tuning fork, your voice imitating the tuning fork, and your interesting sound. Make sure to write what your interesting sound WAS in your report your instructor is curious to know what made the waveform you report! 3
Waveforms and the Speed of Sound (Worksheet) Your Name: Lab Partner(s): 1. In your own words, what is the scientific objective of your measurements today? 2. Tabulate your data in the space provided here. Determining the speed of sound: Δt 1 (s) Δt 2 (s) Δt 3 (s) Δt 4 (s) Δt 5 (s) Δt avg = seconds Your measured value for the speed of sound: seconds 3. Does your measured value for v s agree closely with the accepted value of 343 m/s? What do you think closely means? What do you think is the reason for any discrepancies? 4. Looking at your average value for t and at each of the measured values, do you feel confident in the precision of your results? Why or why not? 4
5. Record your data for the tuning fork measurements here: Frequency printed on the tuning fork: Hz. Period measured from graph for the tuning fork: seconds. Frequency calculated from period: Hz. 6. Does your measured frequency agree with the printed one? (agree to within how much?) 7. What does the waveform look like when you sing the tuning fork s note? Does it matter what vowel you sing with? Can you see more than one frequency at work? 8. Describe what your sound of choice is, and any interesting features you might be able to explain in its waveform. 5