Vibrations and Waves
Amplitude – maximum displacement
from equilibrium
Frequency – number of cycles or
vibrations per unit of time
Period – the time it takes to execute a
complete cycle of motion
http://www.acs.psu.edu/drussell/demos/waves/wavemotion.html
http://www.acs.psu.edu/drussell/Demos/StandingWaves/StandingWaves.html
Fundamental frequency
A guitar string = ½ a wavelength
L
Vibration is greatest at the antinode
So a wavelength is twice the string length... λ = 2L
Velocity = frequency x wavelength, or
now substitute value for f ...
v = fλ or f = v/t
f 1 = v/λ = v/2L
Frequency is inversely proportional to wavelength
Pendulum Lab: http://phet.colorado.edu/en/simulation/pendulum-lab
Longitudinal Sound wave
Or Compression Wave
Sound wave - visual
Visual soundwave
https://www.youtube.com/watch?v=s9GBf8y0lY0
Decibles:
https://www.youtube.com/watch?v=jCQRBJwUt2s
Wave in tub
Harmonics
Harmonics are the integral multiples of the
fundamental frequency
Harmonic series of standing waves on a vibrating string:
frequency = harmonic number X speed of waves
(2)(length of string)
or...
f n = n x v / 2L
Standing waves in an air column:
If both ends are open, all harmonics are
present. Antinodes exist at the end of the
tube (the opposite of strings!)
Distance between nodes = ½ wavelength
or...
d = ½λ
This is the same as a vibrating string... fn = v/2L
Harmonic series
Standing waves in an air column:
Harmonic series
If one end is closed, only odd harmonics are
present. The closed end is a node and the
open end is an antinodes.
Fundamental frequency: f 1 = v/λ = v/4L
Third harmonic has ¾ of a wavelength so λ = 4/3 L
f 3 = v = 3v = 3v = 3f1
λ 4/3L 4L
fn = n x v/4L
v = speed of sound in the tube
n = harmonic number
L = length of tube
Fundamental frequency is the lowest possible
f of a standing wave
Decibels – unit measuring the intensity of sound
Exponential scale
(logarithm)
0 dB = smallest audible sound
10 dB = 101 threshold of good hearing
20 dB = 102 leaves rustling, ticking of watch
30 dB = 103 whisper
40 dB = 104 quiet library
50 dB = 105 moderate rainfall
60 dB = 106 normal voice; dishwasher
70 dB = 107 busy street traffic
80 dB = 108 vacuum cleaner; alarm clock
90 dB = 109 lawnmower; hair dryer, blender
100 dB = 1010 mp3 player at full volume; lawn mower
110 dB = 1011 front row at a rock concert; car horn
120 dB = 1012 police siren
130 dB = 1013 threshold of pain; jackhammer
140 dB = 1014 military jet takeoff; gunshot; fireworks
150 dB = 1015 instant perforation of the eardrum
Amplitude – measureable
Loudness – human perception, duration, frequency
The amount of energy
transported through a medium
is called the intensity of the
wave.
Intensity = Power/area
Unit = watts/meter2
Any sound above 85 dB can cause hearing loss.
Related both to the power as well as length of exposure.
Stereo cilia (really microvilli, contain actin filaments)
Located on the basilar membrane in one of
the three compartments of the Cochlea.
(16,000-20,000 of the hair-like cells)
When broken, the signal is constantly sent to the
brain (tinnitus)
http://www.animations.physics.unsw.edu.au/jw/dB.htm#soundfiles
Sound
NPR – The Sound Book (“Sound Intriguing: The World’s Most Interesting Noises”)
http://www.npr.org/player/v2/mediaPlayer.html?action=1&t=1&islist=false&id=2
74717997&m=274786019
The coolest things sound waves can do
https://www.youtube.com/watch?v=Ude8pPjawKI
William Tell Overture
https://www.youtube.com/watch?v=hxIuIxqo2So
https://www.youtube.com/watch?v=uUpDG680uew