PHYS 256Musical Acoustics

Syllabushttp://bohr.winthrop.edu/faculty/mahes/link_to_webpages/

courses/phys256/phys256home.html

Textbook

The Physics of Sound, 3/E Richard E BergDavid G Stork

Richard E. Berg: B.S, M.S, Ph.D; Professor of Physics, University of Maryland.

B.S in Music with emphasis on piano and clarinet.

David G. Stork: B.S, M.S, PhD; Chief Scientist, Ricoh Innovations, Inc.

Accomplished orchestral and chamber timpanist/percussionist.

Instructor

Ponn Maheswaranathan: B.S, M.S, PhD; Professor of Physics, Winthrop

Native of Sri Lanka, Naturalized U.S. citizen

Fundamental Definitions

1. Position, Length, Distance2. Time3. Velocity or Speed4. Acceleration5. Mass6. Density7. Force8. Pressure

Position, Length, Distance

1. Cartesian Coordinate System (x and y)

2. Prefixes

3. Metric System

http://physics.nist.gov/cuu/Units/index.html

Time

1. Time interval can be measured using the following units: second, minute, hour, day, month, year, etc.

2. The following smaller units are also used: millisecond (ms), microsecond (µs).

3. Calculate the period (T) of a 440 Hz tone.

Speed and Velocity

Speed = Distance/Time

Velocity = Speed + Direction.

Speed of sound in air = 345 m/s = 1100 ft/s

Speed of light = 3x108m/s = 186,000 miles/s.

Acceleration

• Acceleration is the rate at which velocity changes.

t

vv

t

va 0

Units: m/s2, cm/s2

Acceleration due to gravity = g = 9.8 m/s2.

Mass

Mass is a measure of the amount of matter contained in an object.

Examples of MassA massive supertanker, for instance, is one that contains an enormous amount of mass. In comparison, a penny does not contain much mass. Mass is a scalar quantity.

Mass Density

The mass density is the mass m of a substance divided by its volume V:

SI Unit of Mass Density: kg/m3

Linear and areal Density

Linear density of stretched wires is important in the design of stringed instruments.

Linear Density = Mass per unit length.

Areal Density = Mass per unit area.

Force In common usage, a force is a push or a pull.

Forces can be categorized as,

Contact forces and Non-Contact forces.

Newton's Second Law of Motion

mF

a

Newton’s second law is a relationship between acceleration, forces, and mass.

When a net external force acts on an object of mass m, the acceleration a that results is directly proportional to the net force and has a magnitude that is inversely proportional to the mass. The direction of the acceleration is the same as the direction of the net force.

aFm

SI Unit of Force: : kg · m/s2 = newton (N)

Weight

Weight is the force of gravity.

Weight = Mass x Acceleration due to gravity.

On the moon, your weight will be 1/6th of that of Earth weight, because the acceleration due to gravity is 1/6th of that of Earth’s.

http://www.splung.com/content/sid/2/page/gravitation

Units

Quantity SI unit Vector or Scalar

Pressure

People who have fixed a flat tire know something about pressure.

In colliding with the inner walls of the tire, the air molecules (blue dots) exert a force on every part of the wall surface.

Pressure

The pressure P exerted by a fluid is defined as the magnitude F of the force acting perpendicular to a surface divided by the area A over which the force acts:

The SI unit for pressure: newton/meter2 = (N/m2) = pascal (Pa).

Pressure Illustration

Human Ear

Rapid changes in air pressure cause vibrations of the eardrum, which we hear as sound.