Wave Pulses & Superposition
A shape crosses the whole rope while the rope itself stays home, and two pulses pass straight through each other without a scratch.
Introduction
Flick a taut rope once and a hump runs to the far end, while the rope itself stays where it was.
You flick the rope twice as hard, so the pulse is twice as tall. How long does it now take to reach the far end?
What sets the speed
Tension and mass per metre
The speed of a pulse on a stretched string depends on two properties of the rope, its tension and its mass per metre , and nothing else:
Every mechanical wave follows this pattern: a restoring influence on top, an inertia underneath, the square root of the ratio.
The medium stays home
The pulse crosses the whole rope. Watch the beads threaded along it: they sit at fixed values of , and only their heights change.
A single element of the rope is marked at x = 3 m, on its own dashed vertical rail. What does it do as the pulse passes?
What the end does to the pulse
The far end is a ring free to slide up and down a frictionless post. An upright pulse arrives. What travels back?
Two pulses at once
Now a second pulse starts from m at the same instant, upside down, heading the other way. At s the two meet in the middle, and the string is flat from end to end.
At t = 0.25 s the string is flat from end to end. What happens in the next instant?
What comes next
You changed what sets a pulse's speed, flipped it at a clamp, and made two pulses cancel and add. Send pulses continuously instead, and the reflections start arriving back on top of the pulses still going out. Usually the result is a mess, but at certain frequencies it organises itself into a pattern that does not travel at all. That is the next lesson.
Ideas this lesson took on
Each of these is a common intuition the lesson put to the test. If one still feels right, the section that tests it is worth another look.
- “A bigger pulse travels faster”
- “The rope travels along with the pulse”
- “A reflection always comes back flipped”
- “Two pulses that cancel have destroyed each other”
Finished with this lesson?
Progress is stored on this device only. There is no account and nothing is sent anywhere.
Research behind this lesson
- Maurines 1992: Asked what governs how fast a signal runs along a rope or a spring, students explained the speed by the shape of the signal and the manner of its creation, how hard and how fast the flick was, rather than by the properties of the medium.
- Tongchai et al. 2009: The Mechanical Waves Conceptual Survey: 22 multiple-choice items covering propagation, superposition, reflection and standing waves, whose distractors were built from students' own open-ended answers and follow-up interviews rather than invented to look plausible.
- Wittmann et al. 1999: Students reason about a wave pulse as if it were an object, giving it the properties of a thrown ball, expecting the medium to travel with the disturbance.
- Wittmann 2002: Interview and written-response analysis showing students use both event-like and object-like descriptions of wave pulses but reason predominantly from object properties: treating a pulse as a thing with a size and a weight rather than as a disturbance passing through a medium.