3.1.1 Progressive Waves

Key Characteristics of Progressive Waves

1. Amplitude $(A)$:

• The maximum displacement of a point on the wave from its equilibrium position. Amplitude is measured in metres ($m$).

2. Frequency $( f )$:

• The number of complete oscillations passing a point per second. Frequency is measured in hertz ($Hz$).

3. Wavelength $(\lambda )$:

• The distance over which the wave's shape repeats, or the length of one complete wave cycle (e.g., from one peak to the next peak). Wavelength is measured in metres ($m$).

4. Speed $( c$ or $v )$:

• The distance travelled by the wave per unit time. Wave speed is measured in metres per second ($m/s$).

5. Phase:

• The position of a point within the wave cycle, usually measured in radians or degrees.

6. Phase Difference:

• The amount by which one point on a wave lags behind another, measured in radians, degrees, or as a fraction of the wave cycle.

7. Period ($$ T ):

• The time taken for one complete oscillation or one full cycle of the wave. Period is measured in seconds ($s$).

In Phase and Out of Phase

• In Phase: Two points on a wave are in phase if they are at the same position in the cycle (same displacement and velocity) with a phase difference that is a multiple of $360°$ (or $2\pi$ radians). Points in phase have the same frequency and wavelength but do not need the same amplitude.
• Out of Phase: Two points are completely out of phase if they are an odd integer of half cycles apart, meaning their phase difference is $180°$ (or $\pi$ radians). For example, if one point is at the peak of the wave while the other is at the trough.

Equations for Wave Properties

1. Wave Speed Equation:

$$c = f \lambda$$

This equation states that the speed ($c$) of a wave is equal to its frequency ($f$) multiplied by its wavelength (λ).

2. Frequency and Period Relationship:

$$f = \frac{1}{T}$$

The frequency ($f$) of a wave is the inverse of its period ($T$), which is the time for one full oscillation.