Transcript Sound Levels

Music
Physics 202
Professor Vogel
(Professor Carkner’s notes, ed)
Lecture 8
Intensity of Sound
The loudness of sound depends on its
intensity, which is the power the wave
delivers per unit area:
I = P/A
The units of intensity are W/m2
The intensity can be expressed as:
I = ½rvw2sm2
Compare to expression for power in a transverse
wave
Depends directly on r and v (medium
properties)
Depends on the square of the amplitude and
the frequency (wave properties)
Intensity and Distance
Consider a source that produces a sound of
initial power Ps
As you get further away from the source the
intensity decreases because the area over
which the power is distributed increases
The total area over which the power is
distributed depends on the distance from the
source, r
I = P/A = Ps/(4pr2)
Sounds get fainter as you get further away
because the energy is spread out over a larger
area
I falls off as 1/r2 (inverse square law)
Inverse Square Law
Source
r
A1=4pr2
I1 = Ps/A1
2r
A2=4p(2r)2 = 16pr2 = 4A1
I2 = Ps/A2 = ¼ I1
The Decibel Scale
The human ear is sensitive to sounds over a
wide range of intensities
To conveniently handle such a large range, a
logarithmic scale is used known as the decibel
scale
b = (10 dB) log (I/I0)
Where b is the sound level (in decibels, dB)
I0 = 10-12 W/m2 (at the threshold of human
hearing)
log is base 10 log (not natural log, ln)
There is an increase of 10 dB for every factor
of 10 increase in intensity
Sound Levels
Hearing Threshold
0 dB
Whisper
10 dB
Talking
60 dB
Rock Concert
110 dB
Pain
120 dB
Human Sound Reception
 Humans are sensitive to sound over a huge range
 A pain level sound is a trillion times as intense as a sound
you can barely hear
 Your hearing response is logarithmic
 A sound 10 times as intense sounds twice as loud
Thus the decibel scale
 Why logarithmic?
 Being sensitive to a wide intensity range is more useful than
fine intensity discrimination
 Similar to eyesight
 Your ears are also sensitive to a wide range of
frequencies
 About 20 – 20000 Hz
 You lose sensitivity to high frequencies as you age
Generating Musical Frequencies
 Many devices are designed to produce
standing waves
 e.g., Musical instruments
 Frequency corresponds to note
 e.g., Middle A = 440 Hz
 Can produce different f by
 changing v
 Tightening a string
 Changing L
 Using a fret
Music
A musical instrument is a device for setting up
standing waves of known frequency
A standing wave oscillates with large amplitude and so
is loud
We shall consider an generalized instrument
consisting of a pipe which may be open at one or
both ends
Like a pipe organ or a saxophone
There will always be a node at the closed end
and an anti-node at the open end
Can have other nodes or antinodes in between,
but this rule must be followed
Closed end is like a tied end of string, open end is like a
string end fixed to a freely moving ring
Sound Waves in a Tube
Harmonics
Pipe open at both ends
For resonance need a integer number of ½
wavelengths to fit in the pipe
Antinode at both ends
L=½ln
v = lf
f = nv/2L
n = 1,2,3,4 …
Pipe open at one end
For resonance need an integer number of ¼
wavelengths to fit in the pipe
Node at one end, antinode at other
L = ¼l n
v = lf
f = nv/4L
n = 1,3,5,7 … (only have odd harmonics)
Harmonics
in Closed
and Open
Tubes
Beat Frequency
You generally cannot tell the difference
between 2 sounds of similar frequency
If you listen to them simultaneously
you hear variations in the sound at a
frequency equal to the difference in
frequency of the original two sounds
called beats
fbeat = f1 –f2
Beats
Beats and Tuning
The beat phenomenon can be used to tune
instruments
Compare the instrument to a standard
frequency and adjust so that the frequency of
the beats decrease and then disappear
Orchestras generally tune from “A” (440 Hz)
acquired from the lead oboe or a tuning fork