Physics: Wave Motion, Superposition, and Stationary Waves

Comprehensive flashcards reviewing wave motion, progressive/stationary waves, optics, superposition, and wave measurement techniques from lecture notes.

What is a progressive wave?

A progressive wave is an oscillation that travels through matter (or a vacuum), transferring energy from one place to another without transferring any matter.

How do transverse and longitudinal waves differ in their particle oscillations?

In a transverse wave, oscillations are perpendicular to the direction of wave travel. In a longitudinal wave, oscillations are parallel to the direction of energy transfer.

What are the key definitions of wave displacement and amplitude?

Displacement is the distance from the equilibrium position in a particular direction. Amplitude is the maximum displacement from the origin.

How are wavelength, period, and frequency defined for a wave?

Wavelength ($\lambda$) is the minimum distance between two adjacent points oscillating in phase. Period ($T$) is the time taken for one full oscillation to pass a point. Frequency ($f$) is the number of complete oscillations passing a point per unit time.

What is the formula relating wave frequency ($f$) and period ($T$)?

$$f = \frac{1}{T}$$

What is the wave equation relating wave speed ($v$), frequency ($f$), and wavelength ($\lambda$)?

$$v = f \lambda$$

What does it mean for two oscillating particles to be in antiphase?

Particles are in antiphase when they oscillate with a phase difference of $\pi$ radians, meaning they are half a wavelength ($\frac{\lambda}{2}$) out of step with each other.

How can an oscilloscope be used to determine wave frequency?

A wave signal is fed to an oscilloscope using a microphone. The x-axis timebase measures the time taken for one complete oscillation ($T$), which is then used to calculate frequency via $f = \frac{1}{T}$.

What wave properties change during reflection, refraction, and diffraction?

In reflection and diffraction, wavelength ($\lambda$) and frequency ($f$) remain unchanged. In refraction, frequency ($f$) remains constant, but wave speed ($v$) and wavelength ($\lambda$) change.

When does maximum diffraction occur for a wave passing through a gap?

Maximum diffraction occurs when the gap size is equal to the wavelength ($\lambda$) of the incident wave.

Why can longitudinal waves not be polarised?

Longitudinal waves cannot experience polarisation because their direction of energy transfer is already restricted to one plane only, unlike transverse waves whose oscillations occur in many planes perpendicular to travel.

How can a metal grille demonstrate polarisation in microwaves?

When vertically plane-polarised microwaves pass through a metal grille in a vertical orientation, maximum signal passes through. Rotating the grille to a horizontal orientation drops signal to a minimum because free electrons in the metal bars absorb the vertically plane-polarised microwaves.

What is the definition and unit of the intensity ($I$) of a progressive wave?

Intensity is defined as the radiant power passing at right angles through a surface per unit area ($I = \frac{P}{A}$). Its unit is watts per metre squared ($\text{W\,m}^{-2}$).

How is intensity related to distance ($r$) from a point source and wave amplitude?

Intensity is inversely proportional to the square of the radius ($I \propto \frac{1}{r^2}$) and directly proportional to the square of the amplitude ($I \propto \text{Amplitude}^2$).

What is the speed of electromagnetic waves in a vacuum?

$$3.0 \times 10^8\,\text{m/s}$$

What is the formula for refractive index ($n$) in terms of light speed?

$n = \frac{c}{v}$, where $c$ is the speed of light in a vacuum and $v$ is the speed of light in the medium.

What is Snell's Law equation for light passing between two transparent media?

$$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$$

What two conditions are required for total internal reflection to occur?

1. Light must travel from a material of higher refractive index to one of lower refractive index. 2. The angle of incidence to the normal must be greater than the critical angle.

What formula calculates the critical angle ($C$) for refraction from a medium into air?

$\sin(C) = \frac{1}{n}$, where $n$ is the refractive index of the original material.

What is the principle of superposition?

When two waves meet at a point, the resultant displacement at that point is equal to the sum of the displacements of the individual waves.

What does it mean for two waves to be coherent?

Two waves are coherent when they are emitted with a constant and unchanging phase difference.

What phase differences correspond to maximum and minimum resultant displacements in interference?

Maximum displacement occurs when phase difference is an even multiple of $\pi$ radians (constructive interference). Minimum displacement occurs when phase difference is an odd multiple of $\pi$ radians (destructive interference).

What is the Young double-slit equation for determining wavelength?

$\lambda = \frac{a x}{d}$, where $a$ is slit separation, $x$ is adjacent fringe spacing, and $d$ is the distance between slits and screen.

What equation is used with a diffraction grating to find light wavelength?

$d \sin(\theta) = n \lambda$, where $d$ is distance between slits in metres, $\theta$ is angle between 0th and nth maxima, and $n$ is the order of maxima.

How are stationary waves formed?

Stationary waves are formed when two progressive waves with the same frequency (and ideally same amplitude) travelling in opposite directions superpose.

What are nodes and antinodes in a stationary wave?

Nodes are points that always have zero amplitude. Antinodes are points that always have maximum displacement.

What is the distance between two adjacent nodes in a stationary wave?

Two adjacent nodes are half a wavelength ($\frac{\lambda}{2}$) apart.

What boundary conditions occur at the open and closed ends of an air-filled tube for stationary sound waves?

An open end forms an antinode, while a closed end forms a node.

What is fundamental frequency in stationary waves?

The fundamental frequency is the lowest frequency of vibration for a given arrangement, producing the first harmonic.