# 092 Laboratory nine: Mach one: The speed of sound

## Questions

Is there a linear relationship between the time and distance for an echo? What is the speed of sound implied by the time and distance relationship?

## Equipment

• Wood clappers
• Stopwatches
• Distance measuring equipment
• Decent weather.

This lab may take quite a bit of time to gather data in between rain showers.

Laboratory objective: To measure the speed of sound (mach one) by measuring the flight time for an echo.

## Procedure

1. Measure the distance to an echoing surface that is at least 50 meters or more away.
2. Bang the wood clappers in synchronization with the echo. This takes practice and a good ear.
3. Time 30 claps. This is the time for 30 echoes.
4. Record the time and number of claps.

Alternate procedure

1. Utilize an nine member team: clapper, timer, counter, distance measurer, recorder, and four listeners.
2. Measure the distance to an echoing surface that is at least 50 meters or more away.
3. The clapper synchronizes the board claps with the echo. The listeners sit in front of the clapper and use hand signals to indicate whether the board claps are in synch with the echoes.
4. Once synchronization is obtained, the timer starts a stop watch while calling out "Start!"
5. The counter counts the number of claps
6. After a duration of ten seconds the timer calls out "Stop!"
7. The recorder records the number of claps and distance data.

The alternate procedure was developed in March 2008. Both systems produced remarkably similar data, neither system appears to necessarily produce better results. The alternate procedure is easier for the clapper.

The echo flight distance is the distance out-and-back to the surface off of which the echo bounces.

## Data [d] [t]

Location on campus Time for 30 claps (s) Time for one clap (echo travel time) (s) [x] Echo flight distance (m) [y]

Data table for alternate procedure

Location on campus Duration (s) Claps Time for one clap (echo travel time) (s) [x] Echo flight distance (m) [y]
10
10
10
10
10
10
10
10
10
10

Dry bulb temperature: __________

Wet bulb temperature: __________

## Graph [g]

Make an xy scatter graph of the echo travel time [x] versus the double the distance to the echo surface (y). Put the time on the x-axis, and double the distance on the y-axis.

## Analysis [a]

Run an analysis of the graph using the mathematical models decision diagram. Calculate the appropriate values based on your analysis. Is there a mathematical relationship? If linear, is the intercept zero? If linear, what is the slope and intercept?

The points do not have to plot exactly on a line in order for the relationship to be linear. As long as the points scatter equally left and right of the line, do not form a curved pattern, and have a general direction then a linear regression can be calculated. If the sound generally takes more time from greater distances, then there is positive relationship between time and distance, a relationship should be calculated.

The order in which the buildings are encountered during the laboratory does not correspond with the distance to the building. Do not "connect the dots" when setting up the xy scatter graph in the graph wizard. Plot with points only, after the wizard is done add a trend line (linear regression, best fit line, also called least squares line).

The graph is a time (duration) versus space (distance) graph, the slope - if determined - is the speed of the flight of an echo. The slope is the measured speed of sound.

The speed of sound varies with temperature and humidity. Use the dry bulb temperature and the humidity based on the dry and wet bulb temperatures to determine the speed of sound in air at the time of the laboratory. To make this calculation look up the speed of sound in air using the Internet (see the next paragraph) after the laboratory session is over.

WolframAlpha is a knowledge engine that can give you the theoretic speed of sound based on the dry bulb temperature and the relative humidity. Enter the phrase "sound speed ____ Celsius ___% relative humidity" into WolframAlpha and the theoretic speed of sound for that temperature and relative humidity will be calculated.

Use the value from WolframAlpha as a theoretic value and perform an error analysis on the experimental value for the speed of sound from your slope calculations. Run a percentage error analysis against the published value: (measured − theoretical)/theoretical. Do NOT forget the parentheses.

## Conclusion [c]

Write up a discussion of the laboratory including a discussion of the results, the theoretic predictions, whether the experimental data agrees with the theory and how good that agreement might be, and potential sources of error.