MUSICAL ACOUSTICS

Chapter 1

What is Sound?

The Science of Sound

EXAMPLES OF WAVES

Longitudinal waves (air molecules) in a sound wave created by a loudspeaker.

Transverse waves on a rope shaken up and down at one end.

VIBRATING BODIES drum head

air column of a trumpet air in the vocal tract piano soundboard CHANGING AIRFLOW vocal folds opening and closing lips of a brass player siren TIME-DEPENDENT HEAT SOURCE electric spark lightning SUPERSONIC FLOW ”crack” of a rifle bullet sonic “boom”

SOME SOURCES OF SOUND

EXAMPLES OF SOUND SOURCES

(d)  

  

Vibrating drumheadcauses pressure Changes In the air nearby

Holes in a rotatingsiren alternately pass and stop an air stream

Explosion rapidlyHeats the air nearby

Supersonic airplane creates shock waves

Curves of uniform and

changing motion

Shrinking Δy and Δt to obtain instantaneous

speed

Speed as a function of time

GRAPHICAL REPRESENTATION

OF MOTION

Stroboscopic observation of motion:

Constant speed

Increasing speed

Constant speed Increasing speed

DISTANCE BETWEEN TWO POINTS IN A COORDINATE SYSTEM

MOTION

FORCE – can be described as a “push” or a “pull”

Applying a force may result in a distortion, an acceleration, or both

Acceleration is proportional to force: a F

Newton’s second law of motion: a=F/m (or F=ma)

The force of gravity (W) produces an acceleration (9) W=mg (compare F= ma) g=9.8 m/s2 (≈10m/s=2)

Don’t confuse Force and PressurePressure = Force/Area

VIBRATORY MOTIONin which y, v, and a all change with

time

PRESSURE and BUOYANCY

PRESSURE in a containerof fluid: (a) acts on all surfaces; (b) is proportional to depth.

BUOYANT FORCE (dashed arrow) on the immersedobject is due to the excess upward force.

BUOYANCY OF ICE

GRAPHICAL REPRESENTATION OF A SOUND WAVE

WORK AND ENERGY

WORK is average FORCE times DISTANCE moved parallel to the force

W=Fd

If an object with weight mg falls a DISTANCE h, the WORK done by gravity is W=mgh

A baseball moving at speed v has KINETIC ENERGY KE=1/2mv²

An object lifted to a height h above the floor has POTENTIAL ENERGY PE=mgh

POWER

POWER IS ENERGY (or WORK) DIVIDED BY TIME P=W/t

ENERGY IS EXPRESSED IN JOULES (J)

POWER IS EXPRESSED IN WATTS (W)

1 watt = 1 joule/second

UNITS

The preferred system (used all over the world) is the SI (Système International) or mks (meter-kilogram-second) system.

Besides the three basic units (meter, kilogram, second) the system includes such units as newtons, joules, watts, pascals, hertz, etc. which are derived in a logical manner from the basic units.

newtons (force)

energy (joules)

power (watts)

pressure (pascals)

freqency (hertz)