Next: Vibrating Systems
To fully understand the various acoustical aspects of sound production, it is generally necessary to use complex mathematical methods such as calculus. However, it is possible to understand a great deal about the physical aspects of sound production with just a few simple concepts.
- A measure of length between two points.
- Metric system used almost exclusively in this course.
- In two- or three-dimensions, a position is specified in terms of distances along each of two or three independent coordinate axes.
- Speed and Velocity:
- Speed provides a measure of distance traveled over a period of time.
- Velocity specifies both the speed of an object as well as its direction of travel.
- In one dimension, there is essentially no difference between speed and velocity.
- Instantaneous velocity is given by
, where is displacement and is time.
- Acceleration is defined as the rate of change of speed.
- Instantaneous acceleration is given by
- Force = Mass x Acceleration:
- The mass of an object is a measure of its opposition to acceleration.
- Mass and weight are often confused. Weight is the force of gravity on an object. Gravity causes objects to free fall with a constant acceleration (9.8 meters/second on earth). An object's weight will vary depending on a given gravity. An object will have the exact same mass, however, for any gravity.
- Force is typically measured in Newtons (kg meters/second).
- Pressure is defined as the force acting perpendicular to a surface divided by the area of that surface:
- Pressure is a particularly useful quantity to consider when dealing with fluids (liquids and gases), such as air.
- Force = Spring Constant x Displacement: .
- The constant is a measure of the spring's stiffness.
- This linear relationship typically applies only for small displacements.
- The Young's modulus and shear modulus of a material are proportionality constants which relate the resulting deformation to an applied external force.
- For fluids, a similar expression relates a pressure change or stress () and a resulting dilation or volume strain , given by a volume change with respect to the unperturbed volume , via an elastic bulk modulus :
- Work = Force Distance (for a force which is constant in both magnitude and direction).
- When an applied force causes an object to move, work is done by the force.
- Work is typically measured in newton-meters, or joules.
- Power = Work / Time.
- Power relates the rate at which work is done.
- Power is measured in watts (joules/second).
- Generically, the number of times a specified periodic phenomenon occurs within a specified interval.
- In acoustic contexts, we are typically concerned with the frequency of vibrations (of various media), which is measured in Hertz (Hz).
- Vibrations propagate in the form of waves, which involves the transfer of energy through a media.
- The distance between successive waves is referred to as the wavelength.
- Propagation Speed:
- Vibrations travel with different speeds, depending on the media..
- Propagation speed, frequency, and wavelength are related by the relationship: .
- Sound in air travels with a speed roughly equal to 345 meters / second.
- Propagation speed is dependent on the density and elasticity of a media. A more ``massy'' material will have a lower propagation speed. A ``stiffer'' material will have a higher speed of propagation.