Experimental Tests of the Speed of Sound and Human Hearing
Abstract
This series of experiments dealt with observing the speed of sound in air and frequencies and
harmonics present in musical instruments and the human voice.
In the first experiment, the
normal modes of a standing wave within a varying length glass tube were observed and the speed
of sound was calculated.
The observed average speed of sound was 346.45 m/s.
This is
consistent with the accepted approximation of the speed of sound of 345.43 m/s, given a room
temperature of 23 C.
In the second experiment, the resonant frequencies were observed in a
fixed length glass tube open at both sides.
The mode number and frequency were plotted and
the calculated speed of sound was 338.6 m/s.
.
In the third experiment, the structure of musical
scales and the musical frequency standards were analyzed by measuring the frequencies for one
octave of a xylophone and set of tuning forks.
The xylophone was observed to be the C256
standard and the tuning forks the A440 standard.
To observe the phenomenon of beat
frequency, the same note from both instruments was struck and analyzed.
The observed beat
frequency was the absolute value of the difference between their individual frequencies.
We
obtained a result of 18.55 Hz between two sources based on the observed beat period when the
expected difference was 19.84 Hz.
In the final experiment, we analyzed individual voice
harmonics matching the tone of a 256 Hz tuning fork.
Results indicated that each person’s voice
pattern is unique.
Introduction and Theory
A sound wave produces pressure variations in the air that oscillate back and forth.
Each wave
has a unique wavelength and frequency.
The wavelength is the distance between peaks in the
wave.
The velocity (
v
) of this wave can be determined by the equation
vf
λ
=
,
Equation 1.1
where
f
is the frequency and
λ
is the wavelength.
The frequency can be determined by the
equation
f
= 1 / T,
Equation 1.2
where T is the period it takes to make one oscillation.
More complicated waves can occur when
two or more waves occur at the same time in the same medium.
When a sound wave encounters
a fixed boundary, its wave is reflected back in a way that is opposite the original wave.
When
this occurs, there will be times when the waves are out of phase and the waves cancel each other
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View Full Documentout and the point remains stationary.
This is known as destructive interference and the points are
called nodes.
There will also be times when the waves are moving in sync and the resultant
wave will be double the single wave amplitude. The points where this occurs are called
antinodes and the condition is known as constructive interference.
The wave pattern produced
in this circumstance is called a standing wave and can be observed experimentally by directing a
wave of a certain frequency through a glass tube where one end of the tube is open and the other
end is closed and can be adjusted to vary the tube length.
In this case, the open end of the tube
is constrained by outside pressure and must be a node.
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 Spring '08
 Naples
 Physics, Frequency, Wavelength

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