SOUND INTENSITY - DECIBELS

CHECK LAST WEEK’S HOMEWORK

SOUND WAVES – SOME VOCAB

Each cycle of a sound wave includes one condensation and one rarefaction

The frequency of the sound wave is the number of cycles per second that pass by a given location

THE NATURE OF SOUNDA sound with a single frequency is

called a pure tone.A 440 Hz tone consists of 440

condensations, each followed by a rarefaction, every second.

A healthy young person hears frequencies from 20 – 20,000 Hz

THE NATURE OF SOUNDSound intensity, I, is defined as

the sound power, P, that passes perpendicularly through a surface divided by the area, A, of the surface:

THE NATURE OF SOUNDthe threshold of hearing is the

smallest sound intensity that the human ear can detect

~ 1x10-12 W/m2

COMPARING SOUND INTENSITIESWhat if we wanted to compare two

sound intensities?The simplest comparison would be a

ratio of the intensitiesEx: compare I=8x10-12 W/m2 to

I0=1x10-12 W/m2

I/I0= 8x10-12 W/m2 / 1x10-12 W/m2 = 8So I is 8 times as great as I0This does NOT mean that I is 8 times

louder than I0

COMPARING SOUND INTENSITIESWhen a sound wave reaches a

listener’s ear, the sound is interpreted by the brain as being loud or soft

Greater intensities give rise to louder sounds.

But the relationship between loudness and intensity is not a simple linear relationship.

Doubling the intensity does not mean the loudness doubles!

DECIBELSThe decibel (dB) is a measurement

unit used to compare two sound intensities

β is the intensity levelUnits are decibels (dB)Log is the base 10 logarithmI0 is the reference level, usually the

threshold of hearing

DECIBELSEx: compare I=8x10-12 W/m2 to

I0=1x10-12 W/m2

β = 9dBWe can say that I is 9 decibels greater than

I0.

EXAMPLEWhat is the intensity level when I = I0?

β = 0dBSo an intensity level of 0dB does not mean

that the sound intensity I is zero.It means that I = I0

TYPICAL SOUND INTENSITIES AND INTENSITY LEVELS

Intensity (W/m2)

Intensity level dB

Threshold of hearing

1.0x10-12 0

Whisper 1.0x10-10 20

Car without a muffler

1.0x10-2 100

Rock Concert 1.0 120

Threshold of Pain 10 130

PROBLEM SOLVINGSolving decibel problems requires

knowledge of logarithmic functions.logA - logB = log(A/B)

How would we solve for I in terms of β?

I=I0

EXAMPLEHumans can discern a change in

loudness of about 1-3 dB.Doubling the loudness corresponds

to a change of 10 dB. Note that doubling the loudness is

not the same thing as doubling the intensity! (to double the loudness, the intensity needs to increase A LOT)

EXAMPLEOn a dark and scary night, you hear

a sound at 90 dB. A moment later, you hear it again, this time at 93 dB. The corresponding intensities are I1 and I2. How many times greater is the intensity of I2 than I1?

EXAMPLEWhat is the change in sound intensity

needed to double the perceived loudness of a sound?

2 times the loudness means a 10dB increase in sound intensity

So β2-β1=10dB I2/I1 = 10 Intensity must increase by a factor of 10 to get

a sound that is perceived to be twice a loud.Means that a 200W stereo is only twice as loud

as a 20W stereo!

ASSIGNMENT

P. 504 #63-69Due Wednesday.