Types of Waves — Question 10

Question 10

A wave classification should specify what is oscillating

Three observations are made: displacement pulses on a taut cord, a radio signal across an evacuated gap, and a particle detection distribution described by a complex probability amplitude. No claim about local motion direction is supplied.

1. Classify the three descriptions as mechanical, electromagnetic, or matter-wave descriptions and state the relevant physical quantity.

2. Can the labels transverse or longitudinal be assigned to all three merely from this information? Explain which extra geometrical information would be needed for the cord.

Question 10 - Solution

A wave classification should specify what is oscillating

Method and mathematical working

First identify what quantity changes at each point. Only then ask whether a displacement or field vector has a defined orientation relative to propagation.$$\begin{aligned}\text{cord: }\mathbf u&=\mathbf r-\mathbf r_0,\qquad \text{radio: }\mathbf E,\mathbf B,\\\text{matter wave: }P_{\Delta x}&\simeq |\psi|^2\Delta x.\end{aligned}$$

(a) Calculation and conclusion

The cord is a mechanical wave described by material displacement. The radio signal is electromagnetic, described by electric and magnetic fields. The particle description is a matter-wave description, with its amplitude linked to detection probabilities rather than a classical material displacement.

(b) Interpretation and limits

The category alone does not specify the cord displacement relative to its propagation direction. Measuring those two directions is needed to call its motion transverse or longitudinal. A quantum probability amplitude should not automatically be treated as a classical displacement vector; the same geometric labels need a defined physical field.

Physical check

The mechanical/electromagnetic/matter-wave distinction and the transverse/longitudinal distinction answer different questions. Neither can be inferred simply from a wavy-looking curve drawn on a page.