Periodic Waves
Introduced| English |
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| wavelength/ˈweɪvleŋθ/ |
Measuring a wave: how long, how tall, how often
- Keep shaking a rope steadily and you get a train of identical waves marching along.
- To describe it we measure a few key numbers — its length, its height, its rate.
- Together they obey one tidy equation linking speed, frequency and wavelength.
- Master these and you can describe any sound or light wave precisely.
Wavelength, amplitude, period, frequency
- Wavelength 波长 $\lambda$ — the length of one full wave (crest to crest).
- Amplitude $A$ — the height from the middle to a crest (linked to the wave's energy).
- Period $T$ — the time for one full wave to pass a point.
- Frequency $f = 1/T$ — waves per second, in hertz.
A steady wave train
Change the frequency and watch the wavelength change while the speed stays fixed.
Which is the wave equation?
$v = f\lambda$ — speed equals frequency times wavelength.
The distance from one crest to the next is the ____.
One full wave (crest to crest) is the wavelength $\lambda$.
The wave equation
- Speed, frequency and wavelength are linked by $v = f\lambda$.
- In one period the wave advances exactly one wavelength, so $v = \lambda / T = f\lambda$.
- If the speed is fixed (same medium), a higher frequency means a shorter wavelength.
- This single relation ties together every wave quantity.
A wave has frequency $50\ \text{Hz}$ and wavelength $2\ \text{m}$. What is its speed, in $\tfrac{\text{m}}{\text{s}}$?
$v = f\lambda = 50 \times 2 = 100\ \tfrac{\text{m}}{\text{s}}$.
At a fixed wave speed, a higher frequency means a:
$v = f\lambda$ with fixed $v$: higher $f$ gives shorter $\lambda$.
Select all true statements about periodic waves.
$f = 1/T$, amplitude carries energy, and $v = f\lambda$. Wavelength is a length, not the height (that's amplitude).
Reading it in sound and light
- For sound, frequency is pitch and amplitude is loudness.
- For light, frequency is colour and amplitude relates to brightness.
- A high-pitched note and blue light both have a high frequency (short wavelength).
- The wave equation applies to them all — just plug in the right speed.
When a wave enters a new medium, its frequency stays the same while its speed and wavelength change.
Frequency is set by the source and is unchanged; $v$ and $\lambda$ change together.
When a wave passes into a new medium, its speed and wavelength change, but its frequency stays the same (it is fixed by the source). So use $v = f\lambda$ carefully: the frequency is the constant, and $v$ and $\lambda$ change together.
A wave has frequency $50\ \text{Hz}$ and wavelength $2\ \text{m}$. Find its speed.
- $v = f\lambda = 50 \times 2 = 100\ \tfrac{\text{m}}{\text{s}}$.
Double the frequency (same medium) and the wavelength halves to keep $v$ the same.
A periodic wave is described by its wavelength $\lambda$, amplitude $A$, period $T$ and frequency $f = 1/T$. They obey the wave equation $v = f\lambda$. Entering a new medium changes $v$ and $\lambda$ but keeps $f$ fixed. For sound, $f$ is pitch; for light, $f$ is colour.