Physics 175: Physics of Musical Sound

Class Organization

• 1-2:15pm MWF

• Class time spent in demos, some lecturing, and discussions
• Roughly every 2 weeks we have lab on Friday
• Lab time spent hands-on as much as poss.
• You are responsible for keeping up with the reading--I will NOT be presenting it all.

Coursework and Grading

• 11 homeworks, ~1 per week (44%)

• Includes attending four concerts and reporting on them (email)
• 8 quizzes (most Mondays) (16%)
• Two 1-hour in-class, open-book exams each worth 10% (weeks 8 and 13)
• Final Group Project/Presentation —given Thursday 12/19 afternoon (12%, group grade)
• Short final paper on project (8% individual)

Physics of Musical Sound

• Sound as Physical Motion

• Sound as Music
• Sound as Wave Motion
• Sound Perception and Acoustics
• Sources of Musical Sound
• Sound Reproduction

Sound as Physical Motion

• Pressure--Pascals or Nm-3

• 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

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

Physical Quantities we Need

• Distance

• Velocity
• Acceleration
• Force
• Work
• Energy
• Power

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 300m s^-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. 1 N = 1 kg m s^-2 . I.e. 1 N will give a mass of 1 kg an acceleration of 1 m 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. 1 J = 1 N m = 1 kg 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. 1 Watt = 1 Joule/second = 1 J 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 J/m²/s or W m^-2 .

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.
• 1000W/m2 = 10³W/m²
• 0.000000000001W/m²=10^-12W/m²
• 1,000,000,000,000,000:1=10¹⁵:1
• Familiarize yourself with the wikipedia article
• http://en.wikipedia.org/wiki/Scientific_notation

Scientific Notation

• Format d.ddddx10ⁿ.

• d’s called significant figures. We use about 3.
• Converting numbers >10
• Copy all the leading digits till reach zeros
• Put new decimal point after first digit.
• Write x10ⁿ where n is 1 less than number of digits to left of original decimal point.
• Eg. 1270000 = 1.27x10⁶.
• Eg. 4.29x10³ = 4290.
• Eg. 6.3756x10² = 637.56.