4.4WavesFoundation

Progressive Waves

From the ripples on a pond to the light reaching your eyes from a distant star, every travelling wave shares the same handful of describing quantities. Master these definitions and the single equation linking them, and you have the vocabulary for the entire waves module.

35 min Video by Understanding A Level Physics by Dave Module 4.4 Waves

A Level Physics: Progressive WavesWatch the full walkthrough before the notes below.

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What you'll be able to do

Define displacement, amplitude, wavelength, period and frequency for a progressive wave
Use the wave equation $v = f λ$
Define phase difference between two points on a wave
Use $T = \frac{1}{f}$

Describing a progressive wave

A $progressive wave$ transfers energy from one place to another without any net transfer of the medium’s particles. $Amplitude$ is the maximum displacement from the equilibrium (undisturbed) position; $wavelength$ , $λ$ , is the distance between two adjacent points in the same phase (such as two adjacent peaks); $frequency$ , $f$ , is the number of complete waves passing a point per second; and $period$ , $T$ , is the time for one complete wave cycle.

T = \frac{1}{f}

Period and frequency are reciprocals of each other.

The wave equation

Wave speed, frequency and wavelength are linked by the wave equation, valid for any type of progressive wave.

v = f λ

Wave speed = frequency × wavelength.

1Rearrange

v = f λ

λ = \frac{v}{f}

λ = \frac{340}{440}

Answer

λ \approx 0.77

Phase difference

$Phase difference$ describes how far out of step two points on a wave (or two separate waves) are, expressed either in degrees, radians, or as a fraction of a full cycle. Two points exactly one wavelength apart are in phase (zero phase difference); points half a wavelength apart are in antiphase (180° or $π$ radians out of phase).

1Fraction of a wavelength:

\frac{0.15}{0.60} = 0.25

(a quarter wavelength).

2A full wavelength corresponds to 360°, so phase difference

= 0.25 \times 360°

Answer

90°

(a quarter of a cycle out of phase)

Tip — Phase difference only depends on the separation as a FRACTION of a wavelength — the same physical separation gives a different phase difference for a different wavelength.

Equation recap

v = f λ

The wave equation.

T = \frac{1}{f}

Period and frequency.

Common mistakes to avoid

Believing a progressive wave transports the medium’s particles from source to destination.

A progressive wave transfers ENERGY, not matter — particles of the medium oscillate about a fixed position but do not travel with the wave.

Assuming a fixed physical separation always gives the same phase difference.

Phase difference depends on separation as a FRACTION of the wavelength — the same distance means a different phase difference for waves of different wavelength.

Confusing period and frequency.

Period (T, in seconds) is the time for one cycle; frequency (f, in Hz) is cycles per second — they are reciprocals, T=1/f.

Key takeaways

A progressive wave transfers energy without net transfer of matter.
Wave equation: v = fλ.
Period and frequency are reciprocals: T = 1/f.
Phase difference depends on separation as a fraction of the wavelength.

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Progressive Waves

35 min Video by Understanding A Level Physics by Dave Module 4.4 Waves