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Physics Section 12.3
Apply the properties of sound resonance
Recall: A standing wave is the result of the superposition of a
wave and its reflection from a fixed termination.
A taut string can vibrate many different ways.
When a string vibrates as a whole, it vibrates at its
fundamental frequency. The length of the string is ½
the wavelength.
Harmonics are whole number multiples of the
fundamental frequency.
Examples of harmonic frequencies:
fundamental (1st)harmonic
100 Hz
2nd harmonic
200 Hz
3rd harmonic
300 Hz
4th harmonic
400 Hz
Harmonic frequencies generated by a string
fn = n v_
2L
n = harmonic number
v = speed of wave on string (m/s)
L = length of string (m)
fn = frequency of the harmonic (Hz)
example
What is the fundamental frequency of a string that is
.50 m long when the wave travels at a speed of 65
m/s? What is the frequency of the 6th harmonic?
Standing waves can be created in a column of air in a tube. There are two types of air columns.
Harmonic frequencies generated by an open tube
fn = n v_
2L
n = harmonic number
v = speed of wave in air (m/s)
L = length of open tube (m)
fn = frequency of the harmonic (Hz)
example
The speed of sound in an open tube is 340 m/s. The
length of the tube is .40 m. Find the frequencies of
the 1st three harmonics.
Closed tube harmonics
Harmonic frequencies generated by an closed tube
fn = n v_
4L
n = harmonic number
v = speed of wave in air (m/s)
L = length of closed tube (m)
fn = frequency of the harmonic (Hz)
examples
Find the length of a
closed tube whose 3rd
harmonic is 1200 Hz
when the sound speed
is 340 m/s.
At what lengths will a
sound with a frequency
of 512 Hz resonate?
The number and mixture of harmonics present in a
sound is referred to as the spectrum of the sound. The
listener detects harmonics as the quality or timbre of
the sound.
Recall: frequency determines the pitch of a sound…musical scales consist of 12 notes, each
at a given frequency. The frequency of the 13th note is double the frequency of the 1st note.
A sound with a frequency that is twice another sound
is one octave higher in frequency.
Frequency A
Frequency B
Frequency C
Frequency D
100 Hz
200 Hz (one octave higher than A)
400 Hz (two octaves higher than A)
800 Hz (three octaves higher than A)
An other feature of superposed waves is called beats. Consider two waves of slightly
different frequencies superposed.
Beats are the periodic variation in the amplitude of a
wave that is the superposition of two waves with
slightly different frequencies.
The number of beats per second is equal to the difference
between the frequencies.
example
Two waves of frequencies 8 Hz and 10 Hz are
superposed. Find the number of beats per second.
An oscilloscope is a device that can be used to analyze any electrical output.
If a microphone is attached to an oscilloscope, sound waves can be analyzed.
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The Oscilloscope
What is an oscilloscope, what can you do with it, and how does it work? This section
answers these fundamental questions. The oscilloscope is basically a graph-displaying
device - it draws a graph of an electrical signal. In most applications the graph shows how
signals change over time: the vertical (Y) axis represents voltage and the horizontal (X) axis
represents time. The intensity or brightness of the display is sometimes called the Z axis.
(See Figure 1.) This simple graph can tell you many things about a signal. Here are a few:
You can determine the time and voltage values of a signal.
You can calculate the frequency of an oscillating signal.
You can see the "moving parts" of a circuit represented by the signal.
You can tell if a malfunctioning component is distorting the signal.
You can find out how much of a signal is direct current (DC) or alternating current (AC).
You can tell how much of the signal is noise and whether the noise is changing with time.
What Can You Do With It?
Oscilloscopes are used by everyone from television repair
technicians to physicists. They are indispensable for anyone
designing or repairing electronic equipment. The usefulness of
an oscilloscope is not limited to the world of electronics. With
the proper transducer, an oscilloscope can measure all kinds of
phenomena. A transducer is a device that creates an electrical
signal in response to physical stimuli, such as sound, mechanical
stress, pressure, light, or heat. For example, a microphone is a
transducer.
An automotive engineer uses an oscilloscope to measure engine
vibrations. A medical researcher uses an oscilloscope to measure
brain waves. The possibilities are endless.
How does an oscilloscope work?
An outline explanation of how an oscilloscope works can be given using the block diagram shown
below:
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Like a televison screen, the screen of an oscilloscope consists of a cathode ray tube. Although
the size and shape are different, the operating principle is the same. Inside the tube is a
vacuum. The electron beam emitted by the heated cathode at the rear end of the tube is
accelerated and focused by one or more anodes, and strikes the front of the tube, producing
a bright spot on the phosphorescent screen.
The electron beam is bent, or deflected, by voltages applied to two sets of plates fixed in the
tube. The horizontal deflection plates, or X-plates produce side to side movement. As you
can see, they are linked to a system block called the time base. This produces a sawtooth
waveform. During the rising phase of the sawtooth, the spot is driven at a uniform rate from
left to right across the front of the screen. During the falling phase, the electron beam
returns rapidly from right ot left, but the spot is 'blanked out' so that nothing appears on the
screen.
In this way, the time base generates the X-axis of the V/t graph
assignment
• Page 431
• Problems 1 - 5