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Speed of Sound in Air

Equipment

1  Sound Sensor w/Extension Cord  CI-6506 1  Economy Resonance Tube  WA-9495 1  Large Rod Base  ME-8735 1  45 cm Rod  ME-8736 1  Multi Clamp  ME-9507 1  Pulley Mounting Rod  SA-9242

Required but not included:1  Tape Measure (metric)

Introduction

The purpose of this activity is to measure the speed of sound in air using a tube that is closed at one end. Use a Sound Sensor to record the initial pulse of sound and its echo. Calculate the speed of sound based on the overall distance traveled and the round-trip time.

Background

The speed of sound is different in different materials. The speed depends on the elastic modulus and the density of the material. For example, the elastic modulus of helium is about the same as the elastic modulus of air, but the density of helium is much less. Therefore, the speed of sound in helium is about three times faster than the speed in air. Sound waves travel through air much like waves travel across the surface of a lake or pond: at a fixed speed, being redirected by interactions with dissimilar objects. Much like waves on a pond are reflected off solid objects like the hull of a boat or a dock, sound waves can also be reflected or redirected.

Figure 1: Speed of Sound in Air

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Setup

1. Set the resonance tube on the lab table and extend it to some arbitrary length. Do not make the length so long that the tube hangs off the end of the lab table or impedes other lab groups.

2. Mount the pulley mounting rod to the side of the sound sensor using the threaded socket.

3. Place the 45 cm rod vertically into the rod base, and then use the multi clamp to mount the sound sensor and pulley mounting rod at a right angle.

4. Adjust the position of the rod base and sensor so that the front of the sound sensor is just at the opening of the tube and is pointed down its length.

5. Plug in the sound sensor to Ch. A on the interface.

6. In PASCO Capstone, set the sample rate to 20 kHz. Create a graph of Sound Intensity vs. Time. Then set a measurement-base start condition: Sound Intensity is above 5 V. Set a stop condition for the time of 0.05 s.

Figure 2: Mounting the Sound Sensor

Procedure

1. Use the tape measure to measure the length of the tube.

2. Click the record button below. Data will not appear in the graph until data collection is triggered by a loud sound near the sound sensor. Data collection will automatically stop after 0.05 seconds.

3. After clicking record, have a group member snap her/his fingers near the opening of the tube.

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4. It should be clear in your data when the initial sound from the snap reached the sound sensor, and when the echo from the end of the tube was returned. Use the delta tool to determine the time between the initial sound and the echo. Record this time.

5. Repeat the same procedure two more times. Record the echo times.

6. Calculate the average value of your echo times. Use that average value and the path length of the sound wave to determine an experimental value for the speed of sound in air.

HINT: The path length of the sound wave is not equal to the length of the tube. Analysis

1. The speed of sound in air is temperature dependent. This theoretical value can be calculated using

v = 331 m/s + 0.6 T

where T is the temperature of the air in degrees Celsius. If you can measure the air temperature, calculate the actual speed of sound. Otherwise, use 343 m/s which is based on 20oC.

2. Calculate the percent error between your experimental value for the speed of sound in air and the actual value. Record your percent error in the box below.

% Error=|Actual−Experimental|Actual

× 100 %

3. What caused the error in your experimental value for the speed of sound in air, and what could you have done differently to improve the results of this activity?