Download Standing waves lecture

Standing Waves
and the Overtone Series
Standing Waves:
Transverse-Stringed Instruments
and
Longitudinal-Wind Instruments
Transverse Standing Waves
Transverse Standing Waves
A standing wave is an interference effect that can occur
when two waves overlap.
Transverse Standing Waves
A standing wave is an interference effect that can occur
when two waves overlap.
Standing waves can arise with transverse waves, such as
those on a guitar string, and also with longitudinal sound
waves, such as those in a flute.
Transverse Standing Waves
A standing wave is an interference effect that can occur
when two waves overlap.
Standing waves can arise with transverse waves, such as
those on a guitar string, and also with longitudinal sound
waves, such as those in a flute.
In any case, the principle of linear superposition provides
an explanation of the effect, just as it does for diffraction
and beats.
Simulation of Standing waves
http://www3.interscience.wiley.com:8100/legacy/college/cutnell/
0471151831/concepts/index.htm
Standing wave patterns
The Speed of a Wave on a String
The Speed of a Wave on a String
V 
F
W
F = Tension in the string.
W = linear mass or mass per length = m/L.
Problem
The G string on a guitar has a fundamental frequency of 196 Hz
and a length of 0.62 m. This string is pressed against the proper
fret to produce the note C, whose fundamental frequency is 262
Hz. What is the distance L between the fret and the end of the
string at the bridge of the guitar?
Longitudinal Standing
Waves
Musical instruments in the wind
family depend on longitudinal
standing waves in producing
sound. Since wind instruments
(trumpet, flute, clarinet, pipe
organ, etc.) are modified tubes
or columns of air, it is useful to
examine the standing waves
that can be set up in such tubes.
Open tube of air
A pictorial representation of longitudinal standing waves
on a Slinky (left side) and in a tube of air (right side) that
is open at both ends (A, antinode; N, node).
Closed tube of air
A pictorial representation of the longitudinal standing waves
on a Slinky (left side) and in a tube of air (right side) that is
open only at one end (A, antinode; N, node).
Problem
Sound enters the ear, travels through the auditory canal,
and reaches the eardrum. The auditory canal is
approximately a tube open at only one end. The other end
is closed by the eardrum. A typical length for the auditory
canal in an adult is about 2.9 cm. The speed of sound is
343 m/s. What is the fundamental frequency of the canal?
(Interestingly, the fundamental frequency is in the
frequency range where human hearing is most sensitive.)
Sound Intensity
The sound intensity I is defined as the sound power P that
passes perpendicularly through a surface divided by the
area A of that surface:
The unit of sound intensity is power per unit area, or W/m2.
Human Ear and Sensitivity
Audible frequency range: 20 Hz – 20,000 Hz
Audible intensity range: 10–12 W/m2 - 10 w/m2
10–12 W/m2 = Threshold of hearing
10 W/m2 = Threshold of pain
The Sensitivity of the Human Ear
16.8 Decibels
The decibel (dB) is a measurement unit used when
comparing two sound intensities.
The intensity level b (expressed in decibels) relative
to the threshold of hearing, Io is defined as follows:
TABLE 16.2
Hearing
Typical Sound Intensities and Intensity Levels Relative to the Threshold of
Intensity I (W/m2)
Intensity Level b (dB)
Threshold of hearing
1.0 × 10-12
0
Rustling leaves
1.0 × 10-11
10
Whisper
1.0 × 10-10
20
Normal conversation (1 meter)
3.2 × 10-6
65
Inside car in city traffic
1.0 × 10-4
80
Car without muffler
1.0 × 10-2
100
Live rock concert
1.0
120
Threshold of pain
10
130