Physics
Measuring Mach
CLASS SET – PLEASE RETURN - DO NOT WRITE ON
Purpose:
To determine the speed of sound using the concepts of standing waves, interference, and resonance.
Equipment:
Resonance Tube
A large graduated cylinder (500 mL or 1L)
Ruler
Thermometer
Large black rubber stopper or green tuning fork striker
Tuning forkp;
Discussion:
All musical instruments rely on resonance to amplify the sound
originating from a vibrating string as in a guitar, reed as in a
saxophone or set of lips as in a trumpet. For the air inside an
instrument to resonate the air column must vibrate so that an antinode exists at the open end of the column
The tubes in the many instruments are open at both ends. It is possible, however, to resonate a tube
that is open at one end and closed at the other. This is what we will be doing in our lab.
The figures below show examples of air resonating in the closed-end tubes.
Figure 1
Figure 2
Figure 3
The first example above (fig. 1) shows a ¼ λ standing wave. It resonates at the fundamental frequency.
Figure 2 shows a ¾ λ standing wave. It is an overtone (1st harmonic) of figure 1. Lastly, figure 3 shows a
1¼ λ standing wave. It is the 3rd harmonic overtone of the wave in figure 1. Be sure you understand the
wavelengths and overtone concepts before proceeding. In this lab, we will primarily work with the
fundamental frequency for a closed-end tube (fig. 1).
If the fundamental frequency corresponds to a standing wave of ¼ λ, what is the actual wavelength of
the tuning fork in terms of the length of the tube?
Procedure:
STEP ONE:
There should be a graduated cylinder with water in it at your lab station. The tube
should be in the water as well.
STEP TWO:
Select a tuning fork of known frequency. Record that frequency in the data table.
Striking the tuning fork on the rubber stopper, hold the vibrating fork 1 cm above the
empty tube. Move both the fork and tube upward until you hear a louder sound.
Always start with the tube at the lowest position before you begin.
STEP THREE:
Measure the distance from the top of the tube to the water level. Convert from cm to
m. This distance represents the air column needed for resonance. Record your length
in the table.
STEP FOUR:
Measure the diameter of the resonance tube. Convert from cm to m. Record in table.
STEP FIVE:
Find the corrected length of the air column. This will account for the small amount of
air that also vibrates above the tube because the fork cannot come into contact with
the tube. Show your work in the data table.
Length Correction = L’ = 0.3 x tube diameter
Corrected Length = Measured length + Correction
STEP SIX:
Compute the wavelength of the sound wave. Show your work in the data table.
STEP SEVEN:
Using the known frequency and computed wavelength, compute the speed of sound
in air. You must show your work in the data table.
STEP EIGHT:
Determine the actual speed of sound in air. You must show your work in the data
table. The speed of sound in air is temperature dependent. v = 331+0.6T
STEP NINE:
Calculate the percent error for the speed of sound in air.
 v computed  v actual 
% error  
 x 100
v actual


LTHS Physics
Names _____________________________
_____________________________
_____________________________
Period __________
Measuring Mach
Data and Calculations (See Instruction Sheet)
2) Tuning fork frequency
f = ____________
3) Tube length
L = ____________
4) Tube diameter
d = ____________
Calculation of length correction Calculation of corrected length
5) Length correction
Calculation of computed wavelength
6) Computed wavelength
Calculation of speed of sound based on data
7) Speed of sound 1
8) Speed of sound 2
9) Error calculation
Turn Over For Analysis Questions
Room temperature = ________
Calculation of speed of sound based on temperature
Calculation of error:
Group Questions:
Answer the following question with your lab group.
1) How did the two values for the speed of sound compare? Where could the error have come from?
2) A 0.05 meter diameter tube resonates when it is 0.25 m in length. What is the wavelength of the
resonating sound wave? You must SHOW YOUR WORK.
3) If the speed of sound in air is 356 m/s. How long is a 324 Hz sound wave? You must SHOW YOUR
WORK.