Physics of Musical Sound

Sound as Physical Motion

• Pressure--Pascals or Nm-1
• Density--kg m-3
• Velocity--m s-1
• Force--Newtons or kg m s-2
• Frequency--Hertz or Cycles per Second
• Loudness--decibels (dB) or sones

Sound as Music

• Rhythm--note values, time signatures
• Melody--sequence of sounds
• Harmony--relationships between sounds
• Intervals--relationships between notes
• Musical Notation
• Pitched and Unpitched sounds
• Scales and Tunings

Sound as Wave Motion

• Frequency
• Amplitude
• Shape
• Phase
• Superposition--Beats, Interference, Diffraction
• Reflection
• Refraction
• Impedance

Sound Perception and Acoustics

• Timbre--a fancy term for tone color
• Intervals
• Loudness--not as simple as it seems
• Just Noticeable Differences--volume and pitch
• Reverberation--direct and indirect sounds
• What Makes a Good Concert Hall?

Sources of Musical Sound

• Source of Energy--beat, pluck, blow
• Vibrator--generates the actual tone
• Resonator--amplifies, spreads, colors sound
• Pitch, Repetition, and Harmonic Structure
• Percussion
• Plucked, Struck, and Bowed Strings
• Blown Pipes

Sound Reproduction

• Transducer
• Voltage
• Current
• Faraday's Law
• Lorentz Force Law
• Microphone
• Loudspeaker
• Amplifier
• Analog-Digital
• Digital-Analog
• Tape Recording
• CD recording
• Hard/Floppy Disks
• Compression--MP3
• Synthesis

Physical Quantities we Need

Distance

• The normal everyday quantity that measures how far apart two things are.
• Unit the Metre or Meter. 1m = 39+inches
• actually defined by the distance light travels in a given length of time

Velocity

• combines ideas of speed (how fast) and direction into 1 quantity
• defined as distance traveled /time taken
• units metres per second, m s^-1
• important to us because sound travels at a fixed speed of about 300ms^-1

Acceleration

• how fast velocity changes
• defined as change in velocity/time taken
• units m s^-2
• always caused by a force. We cannot feel distance or velocity but we can feel a force and so we can feel acceleration--rollercoaster.
• Most common is accel. due to gravity, 9.8ms^-2.

Force

• a push or a pull, just what we usually mean.
• Units Newtons. 1N = 1 kg m s^-2.
• I.e. 1N will give a mass of 1kg an acceleration of 1m s^-2.
• Newton's First Law says that unless there is a force then a body will stay still or move at constant velocity for ever.
• Forces needed to make air move and give us sound. Need to think where they come from.

Work

• When you push something you do work.
• Defined as Force x Distance moved in direction of force.
• Units Joules. 1J = 1N m = 1kg m² s^-2.
• Don't need it very often but it is a fundamental quantity. Anything we do that is useful requires work!

Energy

• The ability to do work or a measure of the work done.
• Units are same as work, Joules.
• First Law of Thermodynamics says that the Work done by a system is equal to the energy that is lost from the system.
• We can detect sound only because of the energy that the sound carries and we will usually express the strength of sound using energy.

Power

• The rate at which work is done.
• Unit Watts. 1Watt = 1Joule per second = 1J s^-1.
• Power is particularly important for sound. Sound is a continuous process. If we look at one plane in space then, as the sound goes by, energy flows through the plane and we have a power associated with the sound.
• We usually measure the strength of a sound in energy/area/time or
  W/m²/s or W m^-2 s^-1.

Numbers in Physics

• Enormous range of physical quantities
• energy in detectable sound ranges from about 1000W/m2 to 0.000000000001W/m² a range of 1,000,000,000,000,000:1
• Express in Scientific Notation
• pull out powers of 10 to express as a small number x a power of ten.
  E.g. 1560=1.56x10³
• numbers less than 1 are expressed with negative powers.
  E.g. 0.0000263=2.64x10^-5.