Velocity of Sound in Air Goals and Introduction
In this experiment, we will study longitudinal wave motion of sound by determining the velocity of sound in air and using the velocity to find the frequency of a sound wave. Sound in a gas like air is a longitudinal disturbance in the p ressure and displacement of the molecules. It is clear from a simple experiment that sound travels at a relatively relatively fast but finite speed. There is no perceptible delay in the sound that arrives at your ears when a person located across the room is speaking. However, if a lightning flash flash occurs 5 miles away, it takes a significant amount of time before the accompanying thunderclap arrives at your ear. In this experiment, you will examine the relationship between the wave speed, frequency and wavelength of sound, and in the process, make a determination of the speed of sound. You will use standing waves, which are produced when two waves of nearly equal wavelength and amplitude propagate in opposite directions in the same medium. A pattern of loops, or antinodes, is produced, each of which spans one-half wavelength. By measuring the distance between the quiet points, or nodes, in the pattern, you can determine the wavelength (!) of the sound. If the frequency frequency ( f f ) of the sound is known or measured by other means, then the speed (v (v) of the sound waves can be found from the basic wave relation: v= f!
(Eq. 1)
speaker
A
to ear
B
C
D
Figure 1. Resonance Tube Apparatus
Consider the resonance tube shown in Figure Figure 1. Suppose the piston is in position position B. Sound of a certain frequency enters the tube at A from a small speaker. A small amount of the sound entering at A will go through the opening in the piston at B and to your ear (on the far right). Most of the sound energy will will be reflected at B back toward toward A, as in a closed pipe. pipe. For specific lengths of the closed pipe, a standing standing wave is produced and resonance will occur. The sound you hear will be much louder than it would be if the resonant condition did not exist. Standing waves will be produced at various positions of the piston (such as B, C, and D in Fig. 1), for positions that correspond to nodes of the standing waves, as shown in Figure 2.
Figure 2: Standing Waves and Corresponding Wavelengths in a Closed Tube
Note that the distances between successive points of resonance are each one-half wavelength and so the wavelength is twice the distance between resonant points. Thus, if the distance between adjacent nodes, (i.e. the length of one loop) is d , then d = !/2 so the wavelength ! = 2d 2d . For example, if L if L is is the distance between the first and fifth resonant points, it includes four loops and the length of one loop would be L be L/4. /4. Since each loop is half a wavelength, the wavelength would be twice that length: ! = 2( L/4). L/4). The source of sound for the resonance tube shown in Fig. 1 is a small speaker that is driven by an electronic audio oscillator in which the frequency can be closely controlled. A meter stick along the resonance tube helps in recording the positions of successive resonant points.
Goals: Goals: (1) (2) (3)
Measure and consider standing waves caused by various sound waves. Determine the speed of sound in air. Determine the frequency of a sound wave.
Procedure
Equipment – – Kundt’s tube standing wave apparatus, audio oscillator, microphone or hearing tube, meter stick, thermometer 1) Your laboratory instructor will set the oscillator at some specific frequency an d tell you what it is. Record the value as f as f A. 2) Starting with the piston close to the speaker, gradually pull it out, while listening carefully with your ear near the other end of the tube. Find at least three (preferably more) positions of the piston where you hear maximum loudness in the tube. Be careful not to miss any of the maxima. Measure these piston positions and record them as x as xA1, xA2, xA3, etc. 3) Your instructor will set the audio oscillator to another frequency and tell you what it is. Record the value as f as f B. Again find at least three (preferably more) piston po sitions where you hear maximum loudness. Measure these piston positions and record them as x as xB1, xB2, xB3, etc. 4) Your Instructor will set the audio oscillator to a third frequency and tell you what it is. Record the value as f as f C. Again find at least three (preferably more) piston positions where you hear maximum loudness. Measure these piston positions and record them as x as xC1, xC2, xC3, etc. 5) Your Instructor will set the audio oscillator to a fourth frequency , but this time will not tell you what it is. As before, find at a t least three (preferably more) piston positions where you hear maximum loudness. Measure these piston positions and record them as x as xD1, xD2, xD3, etc. 6) Measure and record the room temperature in degrees Celsius as T . As always, be sure to organize your data records for presentation in your lab report, using tables and labels where appropriate. Be sure to label your graphs. Data Analysis
For the frequency f frequency f A, calculate the total distance between the first and last maximum you measured and label it " xA. It will be helpful to use units u nits of meters. Using Fig. 2 as a guide, and noting that the maxima you found correspond to the positions of nodes in the standing waves, determine how many loops of the standing wave lie between the first and last maximum you measured and label it N it N A.
Question 1: Based on Fig. 2, do you expect the distances between successive maxima (e.g. from xA1 to x to xA2, from x from xA2 to x to xA3, from x from xA3 to x to xA4, etc.) to be the same or different? Explain. Do your measurements match your expectation? Explain.
Use the total distance " xA and the number of loops N loops N A to find the length of one loop, and label the result d A. Then use that distance to calculate the wavelength and label it !A. Use Eq. 1 to calculate the speed of sound for this wave and label the result vA. Repeat the same analysis for frequencies f frequencies f B and f and f C to find in each case: the total distance between the first and last maximum (" xB and " xC), the number of loops included ( N N B and N and N C), the length of one loop (d (d B and d C), the wavelength (!B and !C), and the speed of sound (v (vB and vC). Question 2: Given the relationship given by Eq. 1, should the wavelength increase or decrease as the frequency of the oscillator is decreased? Why? Do your data bear out this prediction? Explain.
In the same way, for the fourth (unknown) frequency, find the total distance between the first and last maximum (" xD), the number of loops included ( N N D), the length of one loop (d (d D), and the wavelength (!D). Calculate the mean of your results for v from the three known frequencies frequen cies and label the result vave. Also calculate the standard deviation and the standard deviation of the mean of your results for v. Use your average speed of sound with Eq. 1 to determine the fourth, unknown frequency and label the result f result f D. The predicted speed of sound in air can be approximated by v = 331.3 + 0.606 T m/s, where T is is the air temperature in degrees Celsius. Use this approximation to calculate the predicted speed of sound for your experiment. Label the result v pred. Error Analysis Question 3: Why did we measure the total distance between the first and last maximum (e.g. (e.g. N A), rather than just measure the length of a " xA) and the total number of loops included (e.g. N single loop? Explain why this should result in a more accurate measurement of the period.
Calculate the percentage error of your average experimental speed of sound (v (vave) compared to the predicted value (v (v pred).
Question 4: Remember that the standard deviation of the mean gives you a measure of the experimental uncertainty in your mean value. v alue. Thus, the results would say the true value lies in the range vave ± ! m. Considering your percent error, your mean value, and your standard deviation of the mean, did your you r experimental results confirm the predicted speed of sound? Explain. Questions and Conclusions
Be sure to address Questions 1-4 and describe what has been verified and tested by this experiment. What are the likely sources of error? Where might the physics principles investigated in this lab manifest in everyday life, or in a job setting? Pre-Lab Questions
Please read through all the instructions for this experiment to acquaint yourself with the experimental setup and procedures, and develop any questions you may want to discuss with your lab partner or TA before you begin. Then answer the following questions and type your answers into the Canvas quiz tool for “Velocity of Sound in Air,” and submit it before the start of your lab section on the day this experiment is to be run. PL-1) Two students performing this experiment measure loudness maxima at the following piston positions: 0.17 m, 0.36 m, 0.53 m, 0.71 m, and 0.86 m. How many loops of the standing wave are there between the first and last maximum? PL-2) At another frequency the same two students measure loudness maxima at piston positions of 0.19 m, 0.39 m, 0.60 m, 0.81 m, and 1.00 m. What is the wavelength of the standing wave (in m)? PL-3) At a frequency of 656 Hz, the students determine a wavelength of 0.515 m for the standing wave. What speed of sound do they determine (in m/s)? o
PL-4) The students measure the room temperature to be 18 C. What is the predicted speed of sound in the room (in m/s)? PL-5) Two other students measure the mean and standard deviation of the mean of the speed of sound to be vave = 337.5 ± 3.1 m/s. How does this compare to their predicted value v pred = 343.4 m/s? (A) It is numerically equal to v pred. (B) It is not numerically equal, but it is statistically equal to v pred, because of the standard deviation of the mean.
(C) It is neither numerically nor statistically equal to v pred, because of the standard deviation of the mean. (D) We can’t tell from the information given.
