This presentation will describe a method of measuring the speed of sound. The method involves using tuning forks and listening for resonating standing waves in pipes closed at one end.  PurposePurpose  MaterialsMaterials  Theoretical DerivationTheoretical Derivation  ProcedureProcedure  Data Collection & ResultsData Collection & Results  ConclusionConclusion

Why measure the speed of sound? Sonar, echo location and medical ultrasound all depend on predictions made using the Doppler Effect applied to sound waves. The Doppler effect is the perceived change in frequency of a traveling wave with respect to the relative motion between the wave source and wave observer. The Doppler effect exists because wave speeds are finite. To make predictions using the Doppler effect, the actual speed of the wave in question is necessary. The purpose of this laboratory experiment is to measure the speed of sound in air by listening for resonating standing waves in closed pipes.

 2000 ml Graduated cylinder  Meter stick  ½ inch diameter PVC pipe  Tuning Forks – 256Hz, 512Hz, 1000Hz, 1024Hz  Water Supply  Paper towels  Paper, pencil, calculator, ears & patience The following materials are needed to complete this lab:

Consider a hollow pipe of length L, closed at one end and open at the other. The first four simplest standing wave forms are shown. The simplest one is called the fundamental. The subsequent waves are called harmonics. Notice the pattern between the resonant wavelengths and the length of the closed pipe. A general expression for the standing wavelengths can be written as ; n = positive odd integers

Substituting the general expression for standing wavelength into the wave equation relates wavelengths to frequency and wave speed. Substituted into  This reveals a prediction for the speed of sound in terms of the length of a closed pipe, the frequency of the sound wave, and the n th harmonic.

1.Fill the graduated cylinder 15/16 full of water. 2.Insert the PVC pipe into the water filled cylinder. 3.Activate the tuning fork and hold it ¼ inch above the PVC pipe. 4.Slowly lift the PVC pipe & the tuning fork out of the water filled cylinder. 5.Listen for the fundamental frequency of the sound wave created by the tuning fork to resonate with the air in the pipe.

6.Measure the pipe length from the water level to bottom of tuning fork. 7.Record: a.Frequency of tuning fork b.Harmonic number c.Pipe length 8.Repeat steps 3 -7 for as many harmonics as physically possible with each tuning fork. 9.Change tuning fork frequencies and repeat procedure measuring as many pipe lengths as possible.

Assign group member tasks: Data and Calculations Manager Standing Wave Harmonic Manager Equipment Organizer and Measurement Manager. Laboratory Supervisor Write your data on the front board. Keep the water in the graduated cylinders. Clean up spills. Be quite so others can hear.

Average all the measured values of the speed of sound and compare it to an approximate value of 340 m/s. Discuss: Possible sources of error and mistakes in this experiment. What fundamental physical phenomenon was manipulated to measure the speed of sound in this experiment? What and when to turn in: Each individual student must turn in a completed class data/results table, mathematical model predicting the speed of sound waves from standing wave patterns in closed tubes and meaningful responses to the discussion questions. Due Monday, March 8 th 2004.