Progressive Waves

• The Wave Equation: The speed of a wave ($v$) is the product of its frequency ($f$) and its wavelength ($\lambda$). This fundamental relationship applies to all progressive waves, including sound and light.

Formula: $v = f\lambda$

• Period and Frequency: The period ($T$) is the time taken for one complete oscillation, while frequency ($f$) is the number of oscillations per unit time. They are inversely related: $f = \frac{1}{T}$.

• Phase Difference: This describes the relative position of two points on a wave or two different waves. It is measured in degrees or radians, where one full wavelength corresponds to $360^\circ$ or $2\pi$ radians.

Calculating Phase Difference

• To find the phase difference ($\phi$) between two points separated by a distance $\Delta x$, use the ratio of the distance to the wavelength: $\phi = \frac{\Delta x}{\lambda} \times 360^\circ$
• This method allows you to determine if two points are in phase (moving together) or out of phase.

Determining Wave Intensity

• Intensity ($I$): Defined as the power ($P$) transmitted per unit area ($A$) perpendicular to the direction of wave travel: $I = \frac{P}{A}$.
• Proportionality: For a progressive wave, intensity is directly proportional to the square of the amplitude ($I \propto A^2$) and the square of the frequency ($I \propto f^2$).
• Inverse Square Law: For a point source emitting waves in all directions, the intensity decreases with the square of the distance ($r$) from the source: $I \propto \frac{1}{r^2}$.

• Diagram Precision: When sketching waves, ensure wavelength and amplitude arrows are precisely aligned with peaks and equilibrium lines. Vague or overlapping arrows often result in lost marks.

• Unit Consistency: Always check that frequency is in Hertz (Hz) and wavelength is in meters (m) before calculating wave speed. Be wary of prefixes like $ms$ (milliseconds) or $nm$ (nanometers).

• Proportionality Logic: If a question states the amplitude is tripled, the intensity increases by a factor of $3^2 = 9$. Always square the change factor for amplitude-intensity problems.

• Phase Identification: Points separated by exactly $n\lambda$ (where $n$ is an integer) are in phase. Points separated by $(n + 0.5)\lambda$ are in antiphase ($180^\circ$ out of phase).

• Matter Transfer: A common error is believing that the medium (like air or water) moves along with the wave. Remember that the medium only vibrates; only the energy moves forward.

• Wave Speed vs. Particle Speed: The speed of the wave ($v$) is constant in a uniform medium, but the speed of individual particles varies as they oscillate (reaching zero at maximum displacement).

• Frequency vs. Medium: The frequency of a wave is determined by the source, while the speed of the wave is determined by the properties of the medium it travels through.