Principle of superposition of waves and formation of stationary waves Flashcards – AQA A-level Physics (7408)

How do two travelling waves form a stationary wave?

They have the same frequency, travel in opposite directions and superpose.

How can the formation of a stationary wave be shown graphically?

Add the two travelling waves’ displacements point by point at successive times.

For two equal-amplitude waves forming a stationary wave, what are nodes and antinodes?

Nodes have zero resultant displacement at all times. Antinodes have the greatest oscillation amplitude.

How does a stationary wave’s displacement profile change over time?

The profile changes as the medium oscillates, but the node and antinode positions remain fixed.

What are the separations between adjacent nodes and between a node and its neighbouring antinode?

Adjacent nodes: half a wavelength. Node to neighbouring antinode: a quarter wavelength.

How do the phases of points in a stationary wave compare within and between neighbouring sections separated by a node?

Points between adjacent nodes oscillate in phase; points in neighbouring sections oscillate in antiphase.

What is the net energy transfer along a stationary wave?

There is no net energy transfer along the wave.

How can reflection produce a stationary wave?

An incident wave superposes with its reflected wave.

How can the stationary pattern of microwaves or sound be detected?

A detector reveals fixed minima and maxima produced by the incident and reflected waves.

How do displacement nodes and antinodes relate to pressure nodes and antinodes in a stationary sound wave?

A displacement node is a pressure antinode; a displacement antinode is a pressure node.

What condition must a stationary wave satisfy at both ends of a fixed string?

Both ends must be nodes.

How is the length $l$ of a fixed string related to the wavelength $\lambda_n$ of its $n$th harmonic?

$l=\frac{n\lambda_n}{2}$, or $\lambda_n=\frac{2l}{n}$.

How many antinodes does the first harmonic of a fixed string have?

One antinode, between the fixed ends.

How do the nodes and antinodes change in successive harmonics of a fixed string?

Successive harmonics have additional nodes and antinodes.

What is the first-harmonic frequency of a string of length $l$, tension $T$ and mass per unit length $\mu$?

$f_1=\frac{1}{2l}\sqrt{\frac{T}{\mu}}$

How does increasing tension, length or mass per unit length affect a string’s first-harmonic frequency?

Increasing tension raises the frequency; increasing length or mass per unit length lowers it.

How is the frequency of the $n$th harmonic related to the first-harmonic frequency?

$f_n=nf_1$