Physics Basics

It is clear that a basic understanding of the nature of sound is needed to truly understand audition, sound systems and music, and to truly know sound you got to know them physics! What I propose here (to myself mainly) is to cover up some basic in physics, focusing on subjects we need to understand sound. The aim is to enhance my knowledge on the subject and share with you guys. Knowledge be free, fly fly little knowledge!

First off we should consider some basics. One we should have in mind is that Physical quantities may be thought of as being Basic or Derived, and either Scalar or Vectors.

The Basic quantities are… well you can think of them as the elemental measurements, of the most fundamental physical laws. The basic quantities that concern us that work with sound are time, length (distance), and massDerived quantities are those that develop from the result of various combinations done with basic quantities and other derived quantities. Includes such phenomenas as velocity, force and work. You’ll see how these derived quantities occur in a bit!

If a quantity can be described completely in terms of just it’s magnitude, it is Scalar. Length is a good exemple of a scalar quantity. On the other hand a quantity is a Vector if it needs to be described by both it’s magnitude and it’s direction. For example; if a body moves 1m from point X1, to point X2, we are considering both magnitude and direction. A derived quantity is a vector if any of its components are vectors, force is a vector because it involves the components of mass (scalar) and acceleration (vector)

Units – don’t get them units wrong

Time (t) is the second (s)

Length (L) is the meter (m)

Mass (M) is the kilogram (kg)

Mass is not the same thing as weight. Mass is related to the density of a body which is the same for that body no matter where it is located. An object’s weight is related to the force of gravity upon it so that weight changes as a function of gravitation. A roadie carries both weight and mass, but he only really cares about the weight, don’t get them mixed.

Another thing we have to consider is Inertia – From Newton’s first law of motion; if an object is not moving, then it will tend to remain at rest, if an object is moving in some direction at a given speed, then it will tend to continue doing so. Inertia is the property of mass to continue doing what it is already doing. An outside influence is needed to make a stationary object move, or to change the speed or its direction.

Velocity (v) is the speed at which an object is moving and is derived from the basic quantities of displacement.

Average velocity (meters per second) calculations; If an object leaves point X1, at time T1 and arrives at X2 at t2

velocity

Acceleration (a)  is a change of velocity over time. The velocity of the body at the first point V1 and the time it passes that point is T1. Similarly it’s velocity at the second point and time, respectively, V2 and T2. The average acceleration:

acceleration

Acceleration is expressed in units of meters per second squared! Now that is something hard to get your head around! Try to see it as meter per second per second. So Acceleration is a change of velocity over time, you can also say It is the amount of change in velocity per second.So if an object has an acceleration of 10m/s^2, it means that 10m/s is added to the objects velocity each second.

Force (F) is needed to overcome the body’s Inertia. Force is what causes a mass to be accelerated, that is to change it’s speed or direction. The amount of force is equal to the product of mass and acceleration

Force

Mv – Property of momentum

Force is Measured in Newton’s

Newton

So, lets look at an example. It would take a 2N force to cause a 2kg mass to be accelerated by 1 meter per second squared. Again with the time squared!! Remember, a meter per second square is a meter per second per second, or velocity variation per second, a change in velocity (meter per second) over time (per second)

If two equal forces push in opposite direction, then the net force would be zero, in which case there would be no change in the motion of the object. This is called equilibrium.

The sliding of one body against the other constitutes a force opposing the motion, called friction or resistance. The magnitude of friction between two givens materials is called the coefficient of friction. It is easily understood that the coefficient of friction is greatest for “rough” materials than for “smooth” or “slick” ones.

The second factor that affects the force of friction is heat.  The temperature rise is due to the conversion of the mechanical energy into heat, as a result of the friction. We can accept the amount of heat as an indicator of the amount of friction. Also, the force of friction is equal to the coefficient of friction .

A compressed spring will bounce back to it’s original shape once released. This property of deformed object to return to its original form is called elasticity.  The more “elastic” or “stiff” an object, the more readily it returns to its original form after being deformed. The more a spring is deformed the more it opposes the applied force. The force that opposes the deformation is called restoring force. The restoring force depends on two factors: the elastic modulus of the object’s material and the degree to which the object is displaced. Elastic modulus is the ratio of stress to strain (deformation).

Stress (s) is the ratio of the applied force to the area.

Stress

The resulting relative displacement or change in dimensions (deformation) of the material subjected to the stress is called strain. The restoring force  of an elastic material is equal to the stiffness constant of the material time the amount of displacement, F=Sx.

In a physical sense, work (w) is done when the application of force to a body results in its displacement. Work is quantified in Newton times meters and the unit is the joule (j).

Work

The capability to do work is called energy. The energy of an object in motion is called Kinetic energy, and the energy of a body at rest is its potential energy.  Total energy is the body’s Kinetic energy plugs its potential energy.  Work corresponds to the change in the body’s kinetic energy.

Energy is not consumed but converted. Consider for example a pendulum that is swinging back and forth. Its kinetic energy is greatest when it is moving the fastest, when it passes the middle point. On the other hand, it’s potential energy is greatest at the instant that it reaches the extreme of its swing, when it’s speed is zero.

The rate at which work is done is called Power and it is equal to work divided by time, the unit is the watt and it equal joules per second, 1w=1j/s.

Power

So power is equal to the product of force and velocity. The amount of power per unit of area is called intensity (I). Intensity is measured in watt per square meter, W/m2.

Intensity

In a free field, that is, considering are no reflections, the Intensity of sound decreases with distance from the source according to an orderly rule. Under this condition, increasing the distance from a sound source causes the intensity to decrease to an amount equal to 1 over the square of the change in distance, this principle is known as inverse square lawInverse square law

Doubling the distance from the sound source causes the intensity to drop to 1/4 to the original intensity, tripling the distance causes a 1/9 drop in intensity….

Just as power divided by area yields intensity, so force (F) divided by area yields a value called pressure (p).Pressure is measured in N per meter squared. The unit is the pascal (Pa), where 1Pa=1N/meter squared.

Pressure

I’d like to reference this awesome book by Stanley A Gelfand, Hearing An Introduction to Psychological and Physiological Acoustics. It was my main guide to writing this post.

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