L01. Measuring the Speed of Sound

We'll now guide you in writing your first lab report.  Many of the things you do will be similar for lab reports in the future.

1. Begin your lab report on a clean sheet of notebook paper by writing the title of the lab on the top line.  In the upper-right hand corner, write your first and last names and the name of your school.  If you're working with a partner, write the partner's name in the upper left-hand corner.

2. Below the title, write the goal of the lab exactly as it's given on this page.

A formal lab report would require a discussion of the theory and method of the lab.  However, we're keeping this one informal.  Therefore, you'll move on to the data now.

3. Below the goal, label a section called Data.  Write the first item of data:  frequency of the clock, f = 50.0 Hz

Note that it's not enough to simply say frequency.  You must specify frequency of something.  The short-hand symbol for frequency is also given.  The numerical value is given to you by the instructor, since that's what the frequency of the clock was to the nearest tenth of a hertz.  Note finally that the unit of measurement is given.  Always include units with numerical values of measurements.  In this case, Hz is the unit of frequency and is equal to 1/s or s^-1.  This is equivalent to the unit rotations per second or cycles per second.

4.  Prepare a data table like the following:

The Photo ID is given in the upper-left hand corner of the photo, while the distance is given in the lower left-hand corner.  Note that units of measurement are given in the column headings for measured quantities.  Since the units are in the heading, you don't have to write them again beside the numbers as you fill in the table.  You'll fill in the Angle column as you take measurements.  Later, you'll calculate the value for Elapsed Time.

5. You'll obtain the data used for calculating time intervals from the clock photos that you downloaded and printed. There are two photos taken for each microphone separation, Dd.  These distances are printed on the photographs.  Select a set of four photos with all of them at different distances.  If you're working with a partner, the partner should select the other set of four. 

   For each photo in turn, align the center of the protractor with the center of the disc in the photo.  Align one of the images of the hand on the photo with the baseline of the protractor.  Read the measurement of angle from the other image of the hand.  Be sure to read from 0°.  The diagram to the right shows how to align the protractor. 

   Since the images of the hand have width, you'll need to use a consistent technique for aligning the images with the protractor.  We suggest always using the same side of the hand image as shown by the arrows in the diagram to the right.

Read your measurements to at least the nearest half of a degree.  It's expected that whenever using a measuring instrument that is ruled in divisions, that you read to a fraction of the smallest division.  This fraction will have some uncertainty, but will nevertheless be significant.  (See Chapter 1 of your text for a review of significant figures.)  When you write your measurements, they will be expressed as 35.5° or 22.0° to give two examples.  Note the use of the zero to the right of the decimal point in the latter example.  If you judge the decimal part of the reading to be nearer 0.0 than 0.5, you must express that fact by including the zero.  If you don't, then your reading is judged to be accurate to only the nearest degree. 

Measure the angles for your 4 photos.  Record the angles and the corresponding distances and IDs in the table.

Analysis

You're now ready for the analysis of the data.  Label the section Analysis to begin after your data table.

1. In the prelab, you came up with a formula for calculating the elapsed time between the images of the hand.  If you're working with a partner, discuss your formulas with each other to see if you agree.  If you're not sure about it, you may want to post a question to the Lab and Problem Q&A forum.  Once you've decided on a formula, calculate the elapsed times for the corresponding angles in your table. 

Enter your results in the table.  Also show one complete example calculation in the Analysis section of your report.  That is, begin by writing your formula in symbols.  Then substitute numerical values (with units!) for one of the photos.  Simplify and write the final result (with units!).  You must also express the result to the proper number of significant figures.  Again, see Chapter 1 of your text if you need to review the rule for determining the number of significant figures in a product or quotient of measurements.

Here's an example of a calculation of the area, A, of a triangle given the base, B, and height, H.

A = ½ B∙H

= ½(10.25 cm)(3.30 cm)

= 16.9 cm²

Note that units are included with the measurements as well as the final result.  The latter is rounded to 3 significant figures, because the measurement with the smaller number of significant figures is 3.30 with 3 significant figures.  The trailing 0 is significant, because it specifies that the measurement was made to hundredths of a centimeter.

2. Your data is complete, and it's time to draw a graph.  Use the graph paper that you downloaded and printed.  Before you start, keep in mind these commonly-accepted practices for drawing good graphs.

1. Label your axes with name and units.  For this lab, place Elapsed Time (s) on the horizontal axis and Distance (m) on the vertical axis.  Note that you will never write x and y as axis labels!  Always use the actual names of the variables.

2. Design a decimal-based scale for each axis such that your data will stretch across as much as the available grid space as possible.  By decimal-based scale, we mean a scale such as that used by a ruler.  Take a look at your ruler to see what we mean.  There are 10 divisions between major units of centimeters.  This makes it easy to read measurements in decimals.  Image how much more difficult it would be if there were, say, 7 divisions per centimeter.  On your graph paper, notice that there are 5 minor divisions per major division.  Thus, each minor division is two-tenths of a major division.  Once you've determined a scale for your graph, place equally-spaced numbers along the scale.  You need only number every couple of major divisions.  Also, indicate the position of the origin.

3. Title your graph at the top with the names of the variables in this form:  Distance vs. Elapsed Time for Sound.  Note that the first variable given is the one on the vertical axis.  This is standard scientific form.  Note also that a descriptive phrase is added after the variables.  In this case, the phrase is for Sound.  Units of measurement aren't required in the title.

4. As you plot points on your graph, first locate their coordinates as accurately as you can.  Read to fractions of a minor division.  Think of the graph as an instrument of analysis and use it as such.  At each data point, place a large marker.  We recommend a large X.  You could also use a point, but be sure to surround it with a circle so that it will be easy to locate.

Click here to see an example graph.

Draw your own graph now.

3. As mentioned above, your graph is a tool of analysis.  Theoretically, one would expect the variables of distance and time to have a linear relationship, because the speed of sound is constant.  In reality, your data points may not lie in a straight line because, of course, there are always errors inherent in measurement.  Since we expect the relationship to be linear, however, it makes sense to draw the best straight line through the data.  You do this by placing a ruler or straightedge on the graph in such a way as to split the difference between the data points.  That is, you'll have some above the ruler and some below so that the differences average out to about 0, to the best of your judgment.  When you carry out this process, don't force the line to pass through the origin unless the origin is one of your data points.  In this lab, the origin is not a data point.

Draw your best straight line now.

4. Consider now what information you can obtain by finding the slope of the line that you drew.  You know from math that slope is defined as rise/run or Dy/Dx.  Of course, we don't want to use the symbols Dy and Dx in this or any lab, because those are generic symbols.  For this lab, the rise and the run correspond to Dd and Dt.  Thus, by finding the slope of the graph, you are finding Dd/Dt, which we've seen before is simply the average speed.  When finding the slope of your line, follow the guidelines below in order to obtain the best results.

1. You'll need two points to calculate slope.  Don't select actual data points for this purpose.  Instead, pick two points that are actually on the line that you drew.  In addition, pick points that are far apart.  This will give your result greater accuracy.  In general, greater accuracy is obtained in measuring greater amounts. 

2. Once you've selected the two points, read their coordinates from the axes.  As always, read to a fraction of a minor unit.  Write the coordinates in the usual mathematical form beside each point.

Now select the 2 points that you'll use to calculate slope.

5. In the Analysis section of your report, calculate the slope using the coordinates of the 2 points that you selected.  Show your work completely.  Begin with the formula for slope that applies to this experiment:

v_av = Dd/Dt.

Then express the formula in the form, v_av = (d_f - d_i) / (t_f - t_i).  Substitute numerical values of the coordinates (with units!)  and simplify to find the speed.  As always, give your result with the proper number of significant figures.

Your result is your best value for the speed of sound. 

Questions

After the analysis section, label a section of your report Questions.  Then write answers to the following.  Number your answers with the numbers given below in order to avoid confusion.  When asked for descriptions and explanations, be sure to provide them.  It's also important to express yourself clearly using good English.  Writing well is a skill that is as important for science as for other disciplines.

1. In the first video clip, a stroboscope was used to measure the frequency of the clock.  Describe the technique that was used to ensure that the clock made just one rotation (rather than 2, 3, or more) between flashes of the stroboscope. 

2. We've been using the variable Elapsed Time in the lab.  Clearly state the two events between which the Elapsed Time is measured.

3. There was error inherent in the measurement of distance between the sound triggers shown in the second video clip.  How large do you estimate the error to be...a millimeter, a centimeter, ...?  Give a value and then explain your choice.

4. There was also error inherent in your measurements of angle.  How large do you estimate the error to be in your angle measurements?  Give a value and explain your choice.

Conclusion

To wrap this up, label a section of your report Conclusion.  This is where you summarize what you did and state what you found out.  In summarizing what you did, give an overview of the method used to obtain and analyze data.  Include a description of the method that you viewed in the video clip as well as the method and analysis that you personally carried out.  A good-sized paragraph is usually sufficient to summarize what you did.

Always make it clear whether or not you achieved the goal(s) of the lab.  Be very specific in stating what you found.  In this lab, you were to find the speed of sound, so be sure to state the value (with units!) that you determined.

Review

Before you submit your report, take time to review to make sure it's complete and properly presented.  Review the rubric if necessary.

Submitting Your Work

Be sure to write your name and school in the upper right-hand corner of each sheet of your report.  That includes your graph.  Instructions for faxing your report will be provided before the due date of the lab.

Watch the third video demonstration, Measuring the Speed of Sound Part 2.  The video shows how to use the value of the speed of sound to estimate how long it takes a balloon to burst.