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### Course: AP®︎/College Physics 1>Unit 9

Lesson 2: Wave characteristics

# Wave characteristics review

Review the characteristics of periodic transverse and longitudinal waves such as wavelength, crest, trough, amplitude, expansion, and compression.

## Key terms

Term (symbol)Meaning
Wavelength ($\lambda$)Distance between adjacent maxima or minima of a wave.
Periodic waveWave that repeats over time and space. Also called a continuous wave.
CrestHighest point on a transverse wave. Also called the peak.
TroughLowest point on a transverse wave.
ExpansionA point of maximum spacing between particles of a medium for longitudinal waves.
CompressionA point of minimum spacing between particles of a medium for longitudinal waves.

## Equations

EquationSymbolsMeaning in words
$\lambda =\frac{v}{f}$$\lambda$ is wavelength, $v$ is wave speed, and $f$ is frequencyWavelength is wave speed divided by 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.

### 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
$v=\frac{\mathrm{\Delta }x}{t}$
which we can rearrange to get
$\mathrm{\Delta }x=vt$
Wavelength $\lambda$ 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:
$\begin{array}{rl}\lambda & =vT\\ \\ \\ \lambda & =\frac{v}{f}\end{array}$

## 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.

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:

## Want to join the conversation?

• Is the wave energy proportional to the amplitude? In the practice problem, when two periods of different amplitude but same frequency, the energy of the higher amplitude period is higher. In another problem, two waves of same amplitude and of different frequency have the same energy. By Planck constant, shouldn't the one with higher frequency have more energy?
• I too am confused by the question of how frequency of the wave impacts energy.

Consider this thought experiment:

Person A moves a rope up and down causing a wave to propagate on that rope.

Person B vibrates the rope made of the same material but at twice the rate. This means that the waves will have double the frequency.

Who is expending more energy?

Obviously it is Person B (If in doubt, look to the folks in the gyms who work out with battle ropes. Doing it faster makes you sweat more.)

And by the law of conservation of energy, that energy has to move somewhere. In this case, it moves down the rope.

Therefore , frequency has an impact on the energy.

Can somebody please point out the flaw in this argument?
• "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." But the equation is for velocity (speed) is v= λf, which means that *the higher the frequency and the larger the amplitude, the higher the speed (velocity)*, right? Maybe i am misinterpreting the definition of velocity and speed...
• v=λf is (speed of wave)=(wavelength)(frequency).
Frequency is the number of cycles per second. If you increase the number of cycles in a second, the wavelength of each cycle must decrease.

If you increase frequency, the wavelength must decrease by the same factor. If you decrease the frequency, the wavelength must increase by the same factor.
• Why does changing the frequency does not affect the energy of the wave
• In the classical wave theory, energy of a wave doesn't depend on the frequency of the wave. However, the energy of individual photons in a beam is determined by the frequency of the beam. Wave's energy is directly proportional to the square of its amplitude
• how to calculate lambda,whats the formula?
• Just rearrange the formula given to you to find wavespeed. If you know wavespeed is wavelength x frequency, then rearranging the formula will allow you to find out the wavelength.
• Why does the changing of the frequency not affect the energy of the wave?
• what does 'unchanging medium' mean under 'How to understand the wave speed equation'?
Thanks!
(1 vote)
• To find the velocity of a wave you multiply the wavelength by the frequency, yet if you change the wavelength or frequency the speed is unchanged. Why is the speed unchanged if speed is calculated by the wavelength and frequency and how does a change in medium cause the wave speed to change?
(1 vote)
• I am confused about using the frequency and period formula. Do i treat it like a regular inverse proportion and find a constant?
(1 vote)
• There's no constant in this formula. Frequency is the inverse of period and vice versa. Frequency is the number of wavelengths that passes in one second and period is the number of seconds one wavelength takes to pass.
(1 vote)
• Is it possible for an object to have both longitudinal and transverse wave?
(1 vote)
• no it is not possible
(1 vote)
• How can we associate energy with frequency? i mean ,directly or inversely proportional?
(1 vote)
• I think it is directly proportional, because if you look at some displacement-time graphs, you will see that as the frequency increases, amplitude also increases. Since (amplitude)^2 is directly proportional to the energy a wave carries, it is a direct proportion.
(1 vote)