13.1 Mechanical Pulses and Waves

A mechanical pulse is created when a local disturbance is applied briefly, such as one flick of a rope. Neighboring regions interact through the medium's restoring forces, so the disturbance moves forward even though matter in the rope does not migrate with the pulse. A periodic driving motion generates repeated pulses and forms a continuous wave train.

This pulse-to-wave logic explains why medium properties matter. Greater tension in a string increases restoring force and therefore wave speed. Greater linear mass density increases inertia and slows propagation. The medium controls how rapidly information and energy are passed from one region to the next.

Read lambda from distance between two nearest points in identical phase, such as crest-to-crest. Read T from time between repeated states of one particle. Frequency is cycle count per second. Once any two of (v, f, lambda) are known, the third follows directly.

Unit discipline is non-negotiable in wave questions. Use meters for wavelength, seconds for period, and hertz for frequency before substitution. Most numerical errors in easy wave-equation tasks are unit-conversion errors rather than algebra errors.

A wave transports energy and momentum through coordinated local oscillations. In a rope, each small segment moves mostly up and down around equilibrium while the disturbance moves horizontally. The same separation appears in many systems: local oscillation at one location, organized propagation across locations.

This distinction helps with interpretation questions. If a wave travels right, a given particle can still be moving up, down, left, or right depending on wave type and phase. 'Direction of wave travel' and 'instantaneous direction of particle velocity' are different quantities.