SONOMETER DATA AND THE SPEED OF SOUND
By Joe Laszlo Ph. D.
Background: The data that you collected from Part 2. of the sonometer activity can be used to
calculate the speed of sound. HOW CAN YOU DO THIS?
Part 1. Speed of Sound
The relationship that is used to calculate the speed of sound is:
Speed = frequency X wavelength.
Frequency is the number of vibrations or back and forth motions per one agreed upon unit
of time. The agreed upon unit of time is one second.
Wavelength is the actual physical distance that a wave travels while it is going through one
total vibration.
Why does the Speed of sound = frequency X wavelength?
Suppose you were to consider frequency very generically and rename it events per time unit.
This would be;
f
=
events
time unit
Suppose you were to also consider wavelength very generically and rename it actual distance
traveled per one event.
This would be;
Wavelength
=
actual distance traveled
one event
Now suppose you were to multiply the two quantities:
But first, cancel events in the numerator of the first term by event in the denominator of the
second term. What is remaining?
events
time
X
actual distance traveled
one event
=
distance
time
What is distance divided by time? If you remember back to the previous unit, this calculation
you should give you speed. So you see, the speed of sound in its most generic analysis is still
only distance divided by time!!
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How does this relate to the data from Part 2 of the sonometer activity? First you need to copy the
data from the table you made for Part 2 of the sonometer activity, below. Be sure to leave a
column for the product of each pair of variables. Calculate the speed of sound (the product) by
multiplying the frequency times the wavelength for each pair of variables.
Predictions: Predict how the product of each of the pairs of values that you will be entering into
the data table below will compare before you do the multiplying. Answer below.
Data Table from Sonometer Activity Part 2.
Summary Questions:
1. How do the results of the calculations compare with each other?
Explain why you got the results you did as a result of your calculations.
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2. What is the average of the above-calculated values?
3. How do the lowest and the highest calculated value compare with the average?
4. What is the relationship between the frequency and the wavelength in the speed of sound
formula? (Hint: If one variable increases in what happens to the other variable?)
5. The speed of sound at 0oC = 331 m/sec. Further, the speed of sound changes at the rate of 0.6
m/sec for each 1oC change. The air temperature in the room on the day of the sonometer activity
was_______. What should be the speed of sound at that air temperature?
Are the values that you calculated for the speed of sound from your data reasonable? Explain
your answer.
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Part 2. Additional Considerations of Sound Waves Produced By Vibrating Strings.
Background: Do you remember the shapes of the waveforms that were produced by the wave
machine at Station 2? Figure 1 and 2 below show two examples of what you might have seen
along the whirling string.
Figure 1
A
B
Figure 2
C
D
JRL
If you saw a waveform like Figure 1, this is considered to be an entire transverse wave. The
distance from A to B is considered one wavelength.
Figure 2 is ½ of a transverse wave, in spite of the fact that the distance from C to D the same as
from A to B in Figure 1. The physical distance from C to D is now considered to be ½ of a
wavelength.
1. When String B of the sonometer was open (not being pressed with the fret bar) and plucked,
which waveform did you see, Figure 1 or Figure 2? Write your answer below.
Explain why you answered as you did.
2. Again, referring to the waveforms shown on the above, which one represents one
wavelength? Write your answer below.
Explain why you answered as you did.
Assuming that you answered the two questions above correctly, what additional correction
would you make to the wavelength in the data table in Part 1 of this activity so that the
calculation for the speed of sound might be closer to the actual value at the temperature of the air
on the day of the sonometer activity? Answer below.
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Calculation:
Use any one of the pairs of variables from the data table in Part 1. of this activity and do the
“adjustment” to the wavelength. Then calculate the speed of sound.
Summary Question:
1. How does the new “corrected” value of the speed of sound calculated above compare with the
actual speed of sound in the room on the day of the sonometer activity?
2. Since you still do not seem to get a reasonable answer for the calculation of the speed of
sound, what is there about either sonometer String A or String B. that may be causing this to
occur?
Vocabulary
waveforms
transverse wave
full wave
half wave
frequency
wavelength
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