1.6.14 · D5Oscillations & Waves
Question bank — Wave parameters — amplitude, wavelength, frequency, period, wave speed
True or false — justify
Cover the right-hand side, decide true/false, and say why before revealing.
Amplitude equals the vertical distance from a crest down to a trough.
False. That distance is peak-to-peak, which is . Amplitude is measured from the equilibrium (middle) line to one peak, so it is half of that.
Doubling the frequency of a wave on the same string doubles its speed.
False. Speed is fixed by the medium (tension and density). Doubling forces to halve instead, keeping constant.
Wavelength and period both measure "how often the wave repeats," so they are essentially the same quantity.
False. repeats in space (metres), repeats in time (seconds) — different dimensions. They are only linked through the speed: .
For a given medium, if you know any two of , , you can always find the third.
True. The relation ties all three together, so any two fix the remaining one.
A wave with a larger amplitude must have a longer wavelength.
False. Amplitude (size of the wiggle) and wavelength (spacing of the wiggle) are independent. You can flick a rope higher without changing how far apart the humps are.
If two waves have the same frequency, they must have the same wavelength.
False. Only if they travel in the same medium (same ). A 500 Hz sound and a 500 Hz wave on a string have wildly different wavelengths because their speeds differ.
Frequency and period are inversely proportional, so a graph of against is a straight line.
False. is a reciprocal relation, whose graph is a hyperbola (a curve), not a straight line. A straight line through the origin would mean , the opposite.
In one period, every particle of the medium returns exactly to its starting position and velocity.
True. That is the definition of one full oscillation — after time the particle's state (position and direction of motion) repeats.
The wave speed is the speed at which the medium's particles physically move.
False. is the speed of a point of fixed phase (like a crest) travelling through the medium. The particles themselves only oscillate about their equilibrium; they don't travel with the wave.
Spot the error
Each line contains a flawed statement or step. Find the flaw and state the correct version.
"A buoy swings through 1.2 m total, so its amplitude is 1.2 m."
The 1.2 m is the total (peak-to-peak) swing, which equals . So m, measured from the middle to one extreme.
"Since , a wave with a long period must have a high frequency."
Backwards. A long period means each wobble takes a long time, so few wobbles per second → low frequency. Long ↔ small .
"I raised the frequency, so the crest now travels faster down the string."
The crest's speed is set by the medium and doesn't change. What actually happened is the crests got packed closer together — shrank — while stayed the same.
" only works for sound, not for light."
The relation is universal: it holds for all waves — sound, light, water, string waves. Only the value of differs between media.
"The wavelength is the distance from a crest to the very next trough."
That is only half a wavelength. A full wavelength is crest-to-crest or trough-to-trough — one complete repeat of the shape.
"Speed equals wavelength times period, ."
Wrong combination. Speed is distance per time: (one wavelength per period), which equals since . Multiplying gives the wrong units.
"A 2 Hz wave completes 2 oscillations, so its period is 2 s."
2 Hz means 2 oscillations per second, so each one takes s, not 2 s.
Why questions
Answer in your own words before revealing; the reasoning is what matters.
Why does raising the frequency in a fixed medium shrink the wavelength rather than change the speed?
Because is locked by the medium's properties, and must still hold. If can't move, cranking up forces down to compensate.
Why, in exactly one period, does a crest advance by exactly one wavelength?
After one full oscillation () the whole pattern looks identical, just shifted forward by one space-repeat — and that space-repeat is . So advancing in time equals shifting in space.
Why is frequency the reciprocal of period and not, say, twice the period?
Frequency is "cycles per second." In a time of exactly one period there is exactly 1 cycle, so by direct division.
Why are amplitude and wavelength allowed to be chosen independently?
Amplitude answers "how big is the wiggle?" while wavelength answers "how far apart are the wiggles?" These are separate features of the pattern, so nothing forces one to depend on the other.
Why does a single equation apply to sound, light, and water waves alike?
Because it comes purely from the definition of speed (distance ÷ time) applied to any repeating travelling pattern — no property of a specific medium is assumed in the derivation.
Why can two different observers disagree on a wave's frequency but not on its speed within a medium?
This previews the Doppler Effect: relative motion changes the rate crests arrive (frequency) and their observed spacing, but the wave's propagation speed through the medium is unchanged.
Edge cases
Boundary and degenerate scenarios — the ones formulas quietly assume away.
What is the wavelength of a wave whose frequency approaches zero (a very slow wobble), at fixed ?
From , as the wavelength grows without bound (). The "wave" stretches into an ever-longer, ever-slower disturbance.
What happens to as becomes very large, at fixed ?
: the crests crowd together arbitrarily closely. This is exactly how high-frequency ends of the Electromagnetic Spectrum have the tiniest wavelengths.
If the amplitude of a wave were zero, is there still a wave?
No visible disturbance — every particle sits on the equilibrium line, so there is nothing to see. , , become undefined because there is no repeating shape to measure.
Can the period be zero?
No. would mean an oscillation takes no time, giving (infinite frequency), which is physically impossible — a real medium can't respond infinitely fast.
Does still hold at the instant a wave first starts (a single lone pulse with no repeat)?
A lone pulse has no well-defined or because nothing repeats, yet the pulse still travels at the medium's speed . The relation needs a periodic wave to define and ; the speed itself is always meaningful.
If frequency stays fixed but the wave passes into a medium where is larger, what happens to ?
Frequency is set by the source and is preserved on crossing, so from a larger gives a proportionally larger — the waves spread out in the faster medium.
Active recall
Recall One-line answers
- Amplitude vs peak-to-peak? ::: Amplitude is half the peak-to-peak swing, measured from the middle line.
- Fixed medium, tripled — what happens to ? ::: It falls to one third, since and is fixed.
- Do particles travel with the wave? ::: No; they oscillate in place while the phase pattern travels at .
Connections
- Simple Harmonic Motion — each particle's back-and-forth is the SHM behind period and amplitude.
- Transverse and Longitudinal Waves — every trap here applies to both wave types.
- Speed of Waves on a String — the "medium sets " fact made precise.
- The Wave Equation y(x,t) — where all parameters combine formally.
- Doppler Effect — the observer-disagreement edge cases.
- Sound Waves and Electromagnetic Spectrum — extreme- and extreme- examples.