2 physics of sound

Physics of Sound
Part 1
Sound waves
How they are generated and
travel


Sound Waves


Generation and Propagation


Sound wave = changes in pressure caused by
vibrating object





Sound needs a medium to “vibrate”




Compression = High pressure
Rarefaction = Low pressure
Usually air, but could be anything

Speed of sound depends upon the medium
Air = 1130 ft/sec

Water = 5000 ft/sec Steel = 13000 ft/sec


Measuring sound waves


Sound waves are longitudinal waves





Vibrating object compresses the air around it.
Pushes air away leaving an area of low pressure
Vibrating object then compresses more air to create a
“chain”


Measuring methods
Cycle


A single push and pull of the vibrating object





One are of compression followed by one area of

rarefaction
An initial increase in atmospheric pressure from the
norm, followed by a drop below the norm and then a
return to normal
Mathematically displayed by a sine curve



Pressure on Y axis
Time on X axis


Measuring methods
Period (T) and Frequency (f)



Period - The time it takes to create one cycle
Frequency - The number of cycles in one second

1
f =
T



Measured in Hertz (Hz) or cycles per second


Measuring methods

Example
It takes ¼ sec to create one cycle. What is
the sound wave’s frequency?

1
f =
= 4 cycles per second
.25


Measuring methods


Frequency will determine pitch





High frequency = high pitch
Low frequency = low pitch

Octave – a doubling of halving of the
frequency


Measuring methods


Human hearing range



Low range between 15 to 30 Hz




With enough power lower than 15 Hz can be felt, but
not heard as “sound”

High range varies with age and gender




Women - up to 20 kHz
Men – between 15 to 18 kHz
High frequency range will lower with exposure to high
levels of sound and age


Tuning


Traditional orchestra would tune First Chair Violin A first.





Remaining instruments would tune relative to that
A above middle C was tuned to about 420 Hz
As halls grew larger it was found to be desirable to tune sharper
1939 A was established to be 440 Hz




Corresponds to the 49th key on a full size piano

Tuning is not a science. The relative frequency difference is
what is important


Measuring methods
Wavelength
 The distance from one area of compression
to the next or one area of rarefaction to the
next
v

λ=

f

l=wave length
V = velocity of sound in medium
usually 1130 ft/sec
f = frequency

Measuring methods


Amplitude





How high the pressure goes above and below
normal atmospheric pressure
Corresponds to how loud the sound is
“loudness” is relative to frequency and dependant
on the listener.


Timber and Harmonics



Harmonics – multiples of a base frequency
Timber – the characteristics of a particular sound or
instrument


Different harmonics combined in different levels


Physics of Sound

Part 2
Basic Acoustics
Inverse square law
Reinforcement/cancellation


Interference


Phase







measurement of where the amplitude of a wave is
relative to another wave
A cycle can start at any point in a waveform
Two waves with the same frequency can start at
different times
Measured as an angle in degrees


Related to the sine wave representation of the wave


Interference


Constructive of
destructive interference


Waveforms will add by
summing their signed
amplitude at each instant
in time


Beats




Happens when two
slightly different
frequencies interfere
Often used in tuning


Standing waves






When sound waves bounce off

of obstructions, they can
interfere with themselves
Tends to reinforce some
frequencies and attenuate
others
Prevented by using




Non- Parallel walls, ceilings
Convex surfaces
Multi-level ceiling sections


Reverberance (Reverb)









Consisting of multiple, blended sound images caused by
reflections from walls, ceilings and other structures which do not
absorb sound
NOT echo
 Echo consists of individual, non-blended sound images

Reverb time is related to
 The time it takes for a sound to reduce to an inaudible level
 Loudness of sound relative to background noise
 Ratio of loudness of reverberant to direct sound
Short reverb time (less than 1.5 sec) is better for speech or
drama
Long reverb time (more than 1.5 sec.) is better for music


Absorption




Controlling reflections can reduce or increase reverb
time
Air tends to absorb frequencies above 2K Hz
Sight line obstructions






Frequencies above 10 kHz tend to not bend around
corners well or other obstructions
 l=1.3 inches for 10 kHz tone
Frequencies below 1kHz do very well
 l=5.65 feet for 200 Hz tone

Specialists are often hired to “tune” a space
acoustically


Acoustic attributes




Defined by Leo Beranek after a 6 year study
of 54 concert halls
Used to define acoustic properties in terms
that other trained professionals can
understand


Acoustic attributes


Intimacy – Indicates the size of a room



How it sounds to the listener, not actual size
Determined by the initial-time-delay-gap (ITDG)




Interval between the sound that arrives directly at the

ear and the first reflection

Usually considered to be the most important
attribute


Acoustic attributes


Liveness






Related to Reverberance
Room size is related
More reflections is live. Less reflections is dry or
dead

Warmth



More low frequency sound relative to mid
frequency
Too much low frequency sound is said to be
“Boomy”

Acoustic attributes


Loudness of direct sound





Inverse square law
Loudness of sound will decrease by one quarter
every time the distance from the source is
doubled

Definition or Clarity



Good definition when sound is clear.
Related to intimacy, liveness, loudness of direct
and reverberant sound


Acoustic attributes


Brilliance




A hall that has liveness, clarity and intimacy

Diffusion


Relates to the orientation of reverberant sound




Where is the reflected sound coming from

It is preferable to have reverb sound coming from
all directions


Intensity






Like pitch, loudness is a sensation in the
consciousness of a listener
To produce a sound twice as loud requires
10 times the power
Inverse square law



Sound level is reduced by a factor of the square
of the distance away from the source


If you move double the distance from the source, the
sound intensity will by one quarter