Describing Wave Motion

• Amplitude ($A$): The maximum displacement of a point on the wave from its undisturbed position. It is measured in meters ($m$) and is directly related to the energy or intensity of the wave.

• Wavelength ($\lambda$): The distance between two consecutive identical points on a wave, such as from peak to peak or compression to compression. It is measured in meters ($m$).

• Frequency ($f$): The number of complete wave cycles that pass a fixed point per second. It is measured in Hertz ($Hz$), where $1 Hz = 1$ cycle per second.

• Period ($T$): The time taken for one complete wave cycle to pass a point. It is measured in seconds ($s$) and is the reciprocal of frequency: $T = \frac{1}{f}$.

• Wave Speed ($v$): This is the speed at which energy is transferred through the medium. It is defined as the distance traveled by the wave per unit time ($m/s$).

• Derivation Logic: Since speed is distance divided by time, and one wavelength $\lambda$ travels in one period $T$, the speed is $v = \frac{\lambda}{T}$. Substituting $f = \frac{1}{T}$ gives the fundamental wave equation.

Fundamental Formula: $v = f \lambda$

• Application: This equation applies to all types of waves. If the speed of a wave is constant (determined by the medium), then frequency and wavelength are inversely proportional.

• Check the X-Axis: Always look at the units on the horizontal axis of a wave graph. If the axis is distance ($m$), the distance between peaks is the wavelength. If the axis is time ($s$), the distance between peaks is the period.

• Unit Consistency: Ensure all values are in standard SI units before using the wave equation. Convert $kHz$ to $Hz$ and $cm$ or $mm$ to $m$ to avoid calculation errors.

• Rearranging the Equation: Use a formula triangle or algebraic manipulation to solve for the unknown. For example, $\lambda = \frac{v}{f}$ and $f = \frac{v}{\lambda}$.

• Sanity Check: Remember that for a given medium, wave speed is usually constant. If the frequency increases, the wavelength must decrease proportionally.