Engineering Science - Acoustics (Waves)

What is a wave?

A vibration/oscillation that transfers energy from one point to another.

What are the main types of waves?

• Mechanical waves – exist only in mechanical (physical) medium (e.g. water, air, rock, etc.). Obey Newton’s laws.

• Electromagnetic waves – do not require any physical media to exist (e.g. light, radio waves, microwaves, etc.). These wave travel in vacuum at the speed of light.

• Matter waves – associated with particles behaving like waves (e.g. electrons, protons, even atoms and molecules).

What is a transverse wave?

Motion is perpendicular to the wave’s direction (and parallel to y axis) of travel.

What is a longitudinal wave?

Oscillations are parallel to the direction in which the wave travels.

What is the wave equation for a sinusoidal wave?

y\left(x,t\right)=y_{m}\sin\left(kx-\omega t\right)

This equation gives the displacement, y of string elements at position x for a given time t.

What part of the wave equation is the oscillating term?

\sin\left(kx-\omega t\right)

What part of the wave equation is the phase?

kx-\omega t

What is the amplitude y_m?

Maximum displacement (peak value, extreme high point of y).

What does the phase of the wave tell us?

The stage the wave is at in its cycle.

What is the angular wave number k?

k=\frac{2\pi}{\lambda}

k = the radians per unit distance.

What is angular frequency ω?

\omega=\frac{2\pi}{T}

Rate change of phase.

What are the period T, frequency f and wavelength λ of a wave?

• T = The time for one complete oscillation.

• f = The number of oscillations per second (per unit time).

• λ = Distance between repetitions of the shape of the wave.