Sound Intensity and
Vibrations
Sound Intensity
▪ Rate that energy flows through a given area
– Intensity =
(ΔE/Δt)
=
area
Intensity is Power ÷ area 
P .
area
watt/m2
Equation for the area of a circle = 4πr2
Sound Intensity
▪ Vibrating objects do work on the
air as they push against the
molecules.
▪ Intensity is the rate of energy flow
through an area.
– What is “rate of energy flow”
called?
▪ E/t is called power (P).
– Since the waves spread out
spherically, you must calculate the
area of a sphere. How?
▪ A = 4r2
– So, what is the equation for
intensity?
Sound Intensity
▪ SI unit: W/m2
▪ This is an inverse square relationship.
– Doubling r reduces intensity by ¼.
– What happens if r is halved?
▪ Intensity increases by a factor of 4.
Intensity and Decibels
▪ An intensity scale based on human perception of loudness is often used.
▪ The base unit of this scale is the bel. More commonly, the decibel (dB) is used.
– 0.1 bel = 1 dB,1 bel = 10 dB, 5 bels = 50 dB, etc.
– The lowest intensity humans hear is assigned a value of zero.
▪ The scale is logarithmic, so each increase of 1 bel is 10 times louder.
– An increase in intensity of 3 bels is 1 000 times louder.
Human Hearing
Click below to watch the Visual Concept.
Visual Concept
Threshold of Hearing
Source
Intensity
Intensity
Level
# of Times
Greater Than TOH
Threshold of Hearing (TOH)
1*10-12 W/m2
0 dB
100
Rustling Leaves
1*10-11 W/m2
10 dB
101
Whisper
1*10-10 W/m2
20 dB
102
Normal Conversation
1*10-6 W/m2
60 dB
106
Busy Street Traffic
1*10-5 W/m2
70 dB
107
Vacuum Cleaner
1*10-4 W/m2
80 dB
108
Large Orchestra
6.3*10-3 W/m2
98 dB
109.8
Walkman at Maximum Level
1*10-2 W/m2
100 dB
1010
Front Rows of Rock Concert
1*10-1 W/m2
110 dB
1011
Threshold of Pain
1*101 W/m2
130 dB
1013
Military Jet Takeoff
1*102 W/m2
140 dB
1014
Instant Perforation of Eardrum
1*104 W/m2
160 dB
1016
Intensity
▪ Measured in decibels
– Relative intensity- relating the intensityof a given sound to the intensity a the
threshold of hearing
– Dimensionless because it is a comparison unit
Audible Sounds
▪ The softest sound humans can hear is called the threshold of hearing.
– Intensity = 1  10-12 W/m2 or zero dB
▪ The loudest sound humans can tolerate is called the threshold of pain.
– Intensity = 1.0 W/m2 or 120 dB
▪ Human hearing depends on both the frequency and the intensity.
Vibration & Resonance
▪ Forced vibrations: The tendency of one object to force another adjoining or
interconnected object into vibrational motion
▪ Sympathetic vibrations: a vibration produced in one body by the vibrations
of exactly the same period in a neighboring body
Forced Vibrations
▪ Sympathetic vibrations occur when a vibrating object forces another to
vibrate as well.
– A piano string vibrates the sound board.
– A guitar string vibrates the bridge.
▪ This makes the sound louder and the vibrations die out faster.
– Energy is transferred from the string to the sound board or bridge.
Vibration & Resonance
▪ Natural frequency: The frequency or frequencies at which an object tends to
vibrate with when hit, struck, plucked, strummed or somehow disturbed
▪ Resonance:when one object vibrating at the same natural frequency of a
second object forces that second object into vibrational motion.
Resonance
▪ The red rubber band links the 4 pendulums.
▪ If a blue pendulum is set in motion, only the
other blue pendulum will have largeamplitude vibrations.
– The others will just move a small amount.
▪ Since the vibrating frequencies of the blue
pendulums match, they are resonant.
Resonance
▪ Large amplitude vibrations produced when the frequency of the applied
force matches the natural frequency of receiver
– One blue pendulum was the driving force and the other was the receiver.
▪ Bridges have collapsed as a result of structural resonance.
– Tacoma Narrows in the wind
– A freeway overpass during an earthquake
Resonance (Frequency)
Click below to watch the Visual Concept.
Visual Concept
Human Ear
▪ Transmits vibrations that cause nerve impulses
Pathway = Outer ear (ear canal)Eardrum3 bones (hammer, anvil,
stirrup)CochleaBasilar membranes
Question 1
▪ When the decibel level of traffic in the street goes from 40 to 60 dB, how
much louder does the traffic noise seem?
▪ How much greater is the intensity?
Question 2
▪ Of the following factors:
– Intensity
– Speed of sound waves
– Frequency
– Decibel level
– Wavelength
– Amplitude
Which factors change the loudness of the sound?
Which factors change when pitch gets higher?
Question 3
▪
A tuning fork consists of two metal prongs that vibrate at a single
frequency when struck lightly. What will happen if a vibrating tuning fork is
placed near another tuning fork of the same frequency?