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Wave properties review

Review your understanding of wave properties.

Key points:

A wave is a repeating disturbance that travels through matter or space transferring only energy.
Below is a model of a wave.

A wave’s crest is its highest point, and its trough is its lowest point.
A wave’s amplitude is the maximum distance (positive or negative) a wave reaches from its rest position.
Wavelength is the distance between the same spot on two sections of a wave.
A wave’s frequency can be measured by how many crests (or how many troughs) pass a location in a certain amount of time.
A wave with a larger frequency has more energy. If a wave’s frequency doubles, its energy also doubles.
A wave’s energy is proportional to the square of its amplitude. So, if a wave’s amplitude doubles, its energy increases by four times, because $2^{2} = 4$ ‍.

Some more terms/equation

Term	Meaning
Periodic wave	Wave that repeats over time and space. Also called a continuous wave.
Expansion	A point of maximum spacing between particles of a medium for longitudinal waves.
Compression	A point of minimum spacing between particles of a medium for longitudinal waves.
$λ = \frac{v}{f}$ ‍	$λ$ ‍ is wavelength, $v$ ‍ is wave speed, and $f$ ‍ is frequency

How to identify parts of a wave

Transverse waves

Transverse waves vibrate the particles of a medium perpendicularly to the direction of wave travel to produce the features shown in Figure 1 below.

The crest is another name for the peak of a wave. The amplitude is a measure of the height of the crest.

To be specific, amplitude is defined to be the magnitude of the displacement from the equilibrium center line to the top of a crest. Since the amplitude is a magnitude (and therefore positive by definition), you could measure amplitude from equilibrium to a crest or from equilibrium to a trough.

Longitudinal waves

Longitudinal waves form when the particles of the medium vibrate back and forth in the same direction of the traveling wave. The wave can be visualized as compressions and expansions travelling along the medium. The distance between adjacent compressions is the wavelength.

How to understand the wave speed equation

The speed

v

of a wave is constant for any unchanging medium, so frequency and wavelength are inversely proportional. The wave speed equation is not a new equation, it’s just a different way of writing

v = \frac{Δ x}{t}

which we can rearrange to get

Δ x = v t

Wavelength

λ

is the distance that a wave crest (or trough) travels over one period

T

. We can write period in terms of frequency

f

. Let’s make these substitutions to get:

\begin{aligned} λ & = v T \\ λ & = \frac{v}{f} \end{aligned}

How waves transport energy

Waves carry energy through a medium. Any displacement of the wave is resisted by a directly proportional restoring force. The work to produce a big wave amplitude requires both large forces and displacements, which results in more wave energy.

Therefore, energy transported by a wave increases with the wave amplitude.

Common mistakes and misconceptions

Sometimes people forget that the only way to change wave speed is to change the properties of the wave medium. For example, waves on a string travel faster if you increase the tension of the string. Sound waves travel faster if you increase the temperature of the air. Changing the frequency or amplitude of the waves will not change the wave speed, since those are not changes to the properties of the medium.

Learn more

For deeper explanations of wave characteristics, see the video on properties of periodic waves.

To check your understanding and work toward mastering these concepts, check out our exercises:

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Answer

Oscillations and waves (Essentials) - Class 11th

Course: Oscillations and waves (Essentials) - Class 11th > Unit 3