What is the fundamental difference between transverse and longitudinal waves regarding particle vibration?

In transverse waves, particles vibrate perpendicular to the direction of energy transfer, while in longitudinal waves, particles vibrate parallel to the direction of energy transfer.

How does the measurement of wavelength differ between a transverse wave and a longitudinal wave?

In transverse waves, wavelength is measured from peak to peak or trough to trough; in longitudinal waves, it is measured from the center of one compression to the center of the next.

What is the difference between the period and the frequency of a wave?

The period is the time taken for one complete cycle (seconds), whereas frequency is the number of cycles that occur in one second (Hertz). They are mathematical reciprocals.

Why is it incorrect to define amplitude as the distance from the bottom of a trough to the top of a peak?

Amplitude is defined as the maximum displacement from the *undisturbed* (rest) position. The distance from trough to peak is actually twice the amplitude.

What mistake is made when a student assumes water moves across the ocean with a wave?

The student is confusing energy transfer with matter transfer. Waves transfer energy; the water molecules themselves only move in small circles or up and down, returning to their original spot.

What error occurs if you use a displacement-time graph to measure wavelength?

A displacement-time graph tracks a single point over time, so the horizontal distance between peaks represents the period ($T$), not the wavelength ($\lambda$).

Define 'Amplitude' in the context of wave motion.

Amplitude is the maximum displacement of a point on a wave away from its undisturbed or rest position, measured in metres.

What is the SI unit for frequency, and what does it represent?

The unit is the Hertz (Hz). It represents the number of complete wave cycles or oscillations that pass a point in one second.

State the Wave Equation and define each variable with its units.

$v = f \lambda$, where $v$ is wave speed (m/s), $f$ is frequency (Hz), and $\lambda$ is wavelength (m).

How do you calculate the period of a wave if you know its frequency?

The period ($T$) is calculated by taking the reciprocal of the frequency: $T = 1/f$.

Library Podcasts

Courses

Referral & Rewards

1. Electricity, Energy & Waves

Describing Waves

Summary

Describing waves involves quantifying the physical characteristics of oscillations and their propagation through space and time. This includes defining spatial properties like wavelength, temporal properties like frequency and period, and the relationship between them that determines wave speed.

1. Definition & Core Concepts

Wave Motion: A wave is a periodic disturbance that transfers energy from one location to another without the permanent transfer of the medium's matter. The particles of the medium oscillate about a fixed equilibrium position.
Amplitude ( $A$ ): This is the maximum displacement of a point on a wave from its undisturbed (rest) position. It is measured in metres (m) and represents the 'height' of a peak or the 'depth' of a trough relative to the center line.
Wavelength ( $\lambda$ ): The distance between two consecutive identical points on a wave, such as from one peak to the next or one compression to the next. Like amplitude, it is measured in metres (m).
Equilibrium Position: The central line or 'undisturbed' state where the medium would rest if no wave were passing through it.

A diagram of a transverse wave showing displacement against distance, highlighting the amplitude as the vertical distance from the center to a peak, and wavelength as the horizontal distance between two consecutive peaks.

2. Temporal Properties: Frequency and Period

3. The Wave Equation

4. Key Distinctions in Wave Types

Transverse Waves: The oscillations are perpendicular (at $90^{\circ}$ ) to the direction of energy transfer. These waves feature peaks (crests) and troughs. Examples include light and water ripples.
Longitudinal Waves: The oscillations are parallel to the direction of energy transfer. These waves consist of regions of high pressure called compressions and regions of low pressure called rarefactions. Sound waves are a primary example.

Feature	Transverse Waves	Longitudinal Waves
Vibration Direction	Perpendicular to travel	Parallel to travel
Structure	Peaks and Troughs	Compressions and Rarefactions
Medium	Can travel in vacuums (EM waves)	Requires a medium (particles)

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions