Vibrations, Waves, Sound, and Optics CBT Revision

100 practice flashcards covering SHM, wave propagation, sound, geometrical optics, wave nature of light, and polarization based on Nigerian university physics curriculum.

What is the condition for acceleration when a particle executes simple harmonic motion (SHM)?

Acceleration is proportional to displacement and opposite in direction ($a = -\omega^2 x$).

In the SHM displacement equation $x = A \cos(\omega t + \phi)$, what does the parameter $A$ represent?

Amplitude (the maximum displacement).

How is angular frequency $\omega$ related to frequency $f$?

$$\omega = 2\pi f$$

What is the formula for the period $T$ of a mass-spring oscillator?

$$T = 2\pi \sqrt{\frac{m}{k}}$$

What is the speed of an ideal simple harmonic oscillator at its equilibrium position?

Maximum

What is the velocity of a simple harmonic oscillator at its position of maximum displacement?

Zero

How does the total mechanical energy of an ideal simple harmonic oscillator depend on its amplitude $A$?

It is proportional to $A^2$ ($E = \frac{1}{2} k A^2$).

For a simple pendulum operating at small amplitudes, what physical quantity does the period NOT depend on?

Mass of the bob

What is the phase difference between displacement and velocity in simple harmonic motion?

$\frac{\pi}{2}$ radians ($90^\circ$)

What is the phase difference between displacement and acceleration in simple harmonic motion?

$\pi$ radians ($180^\circ$)

If the spring constant $k$ is quadrupled while mass $m$ remains unchanged, how does the period $T$ change?

It becomes half as large ($T \propto \frac{1}{\sqrt{k}}$).

What defines the critical damping condition in an oscillating system?

It is the condition for returning to equilibrium with the fastest non-oscillatory response.

What is required for the propagation of a mechanical wave?

A material medium

In a transverse wave, how do the medium particles move relative to the direction of wave propagation?

Perpendicular to propagation

In a longitudinal wave, how do the medium particles move relative to the direction of wave propagation?

Parallel to propagation

What fundamental relation connects wave speed $v$, frequency $f$, and wavelength $\lambda$?

$$v = f \lambda$$

How is the wave number $k$ defined in terms of wavelength $\lambda$?

$$k = \frac{2\pi}{\lambda}$$

In which direction does the wave described by $y = A \cos(kx - \omega t)$ propagate?

In the $+x$ direction

In which direction does the wave described by $y = A \cos(kx + \omega t)$ propagate?

In the $-x$ direction

How is phase velocity $v_p$ defined in terms of $\omega$ and $k$?

$$v_p = \frac{\omega}{k}$$

How is group velocity $v_g$ defined?

$$v_g = \frac{d\omega}{dk}$$

What is the relationship between phase velocity and group velocity in a non-dispersive medium?

They are equal ($v_p = v_g$).

What is the standard one-dimensional classical wave equation?

$$\frac{\partial^2 y}{\partial t^2} = v^2 \frac{\partial^2 y}{\partial x^2}$$

How does wave intensity $I$ from an isotropic point source in three dimensions vary with distance $r$?

$$I \propto \frac{1}{r^2}$$

What is the phase difference between two points separated by $\frac{\lambda}{2}$ in a progressive wave?

$\pi$ radians

What type of wave is sound propagating in air?

A longitudinal mechanical wave

What is the approximate audible frequency range for a typical healthy young human?

$20\,\text{Hz}$ to $20\,\text{kHz}$

Which physical wave parameter is pitch most directly related to?

Frequency

What characteristics of a sound wave strongly determine its timbre or quality?

Its harmonic content

What displacement boundary condition exists at the closed end of an organ pipe?

A displacement node

What displacement boundary condition exists approximately at the open end of an organ pipe?

A displacement antinode

What happens to the frequency of a sound wave when it passes from one medium into another?

It remains unchanged (set by the original source).

What formula gives the beat frequency produced by two sound sources with frequencies $f_1$ and $f_2$?

Beat frequency $= |f_1 - f_2|$

If two sound waves have frequencies $f_1 = 256\,\text{Hz}$ and $f_2 = 260\,\text{Hz}$, what is the beat frequency?

$$4\,\text{Hz}$$

What causes the Doppler effect?

Relative motion between the wave source and the observer.

What happens to the observed frequency when a sound source approaches a stationary observer?

The observed frequency is higher than the source frequency.

In which state of matter (gases, liquids, or solids) is the speed of sound generally highest?

Solids

What primary physical principle allows a moving-coil microphone to operate?

Electromagnetic induction

What is the law of reflection relating angle of incidence $i$ and angle of reflection $r$?

$$i = r$$

What are the characteristics of an image formed by a flat plane mirror?

Virtual, upright, laterally inverted, same size as object ($m = 1$).

If an object is placed $2\,\text{m}$ in front of a plane mirror, where is its image formed?

$2\,\text{m}$ behind the mirror

If an object moves $1\,\text{m}$ closer to a plane mirror, by how much does the distance between object and image change?

$$2\,\text{m}$$

How is the focal length $f$ of a spherical mirror related to its radius of curvature $R$ in the paraxial approximation?

$$f = \frac{R}{2}$$

What is the spherical mirror equation?

$$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$

Where is the image formed when an object is placed at the principal focus $F$ of a concave mirror?

At infinity

What type of image is always formed by a convex mirror for a real object?

Virtual, upright, and diminished

If a plane mirror is rotated through an angle $\theta$, through what angle does the reflected ray turn?

$$2\theta$$

What causes spherical aberration in a spherical mirror?

Marginal rays and paraxial rays failing to focus at the exact same point.

How can spherical aberration in a spherical mirror system be reduced?

By using a smaller aperture or parabolic reflector.

How is a ray passing through the centre of curvature $C$ reflected by a spherical mirror?

Back along its original path

Why are convex mirrors preferred for use as vehicle rear-view mirrors?

They provide a wide field of view.

What is Snell's law of refraction?

$$n_1 \sin(i) = n_2 \sin(r)$$

How is the refractive index $n$ of a medium defined in terms of light speed $c$ in vacuum and speed $v$ in the medium?

$$n = \frac{c}{v}$$

What happens to the speed and frequency of light when entering an optically denser medium normally?

Speed decreases while frequency remains constant.

What two conditions must be satisfied for total internal reflection to occur?

Light must travel from a higher to lower refractive index medium, and the incidence angle must exceed the critical angle.

What is the angle of refraction when the angle of incidence equals the critical angle?

$90^\circ$ with the normal

For a medium-to-air interface, what formula relates critical angle $C$ to refractive index $n$?

$$\sin(C) = \frac{1}{n}$$

Which optical principle governs light transmission through optical fibres?

Total internal reflection

What is the thin-lens equation relating focal length $f$, object distance $u$, and image distance $v$?

$$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$

How is lens power $P$ calculated from focal length $f$ given in metres?

$P = \frac{1}{f}$ (in dioptres)

What is the power of a converging lens with a focal length of $+0.50\,\text{m}$?

$$+2\,\text{D}$$

What is the equivalent power $P_{\text{eq}}$ of two thin lenses with powers $P_1$ and $P_2$ placed in contact?

$$P_{\text{eq}} = P_1 + P_2$$

What is the lens maker's formula in air?

$$\frac{1}{f} = (n - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$$

What is Newton's relation for a thin lens, where $x$ and $x'$ are distances from focal points?

$$x x' = f^2$$

How is an optical prism defined?

A transparent optical element bounded by two plane refracting surfaces inclined to each other.

What symmetry exists for a ray traveling through a prism at minimum deviation?

The angle of incidence equals the angle of emergence ($i = e$), and the internal path is symmetric.

What is the approximate deviation $\delta$ produced by a thin prism of angle $A$ and refractive index $n$?

$$\delta = (n - 1)A$$

What relation gives refractive index $n$ in terms of prism angle $A$ and minimum deviation $\delta$?

$$n = \frac{\sin\left(\frac{A + \delta}{2}\right)}{\sin\left(\frac{A}{2}\right)}$$

In normal dispersion through a glass prism, which visible color experiences the greatest deviation?

Violet

Under normal dispersion, how does refractive index $n$ vary with wavelength $\lambda$?

$n$ is larger for shorter wavelengths ($n$ decreases as $\lambda$ increases).

What is angular dispersion in a prism system?

The difference between the angles of deviation for two specified colors.

What optical phenomena combine in raindrops to produce a rainbow?

Refraction, dispersion, and internal reflection

What is the root cause of chromatic aberration in simple single lenses?

Dispersion in the glass, causing different wavelengths to have different focal lengths.

What optical combination is commonly used to correct chromatic aberration in lenses?

An achromatic doublet

What type of spectrum consists of bright spectral lines at discrete characteristic wavelengths?

An emission line spectrum

What type of spectrum features dark lines superposed on an otherwise continuous spectral band?

An absorption spectrum

What is a wavefront?

A continuous surface joining points of equal phase in a wave.

According to Huygens' principle, what does every point on a wavefront act as?

A source of secondary wavelets

What two properties must two light sources satisfy to be coherent?

They must have a constant phase difference and the same frequency.

What path difference $\Delta$ leads to constructive interference between two coherent waves?

$\Delta = m \lambda$ (where $m$ is an integer)

What path difference $\Delta$ produces destructive interference for wavelength $\lambda$?

$\Delta = \left(m + \frac{1}{2}\right)\lambda$ (where $m$ is an integer)

What formula calculates fringe width $\beta$ in Young's double-slit experiment?

$$\beta = \frac{\lambda D}{d}$$

In Young's double-slit setup with $\lambda = 600\,\text{nm}$, $D = 2\,\text{m}$, and $d = 1\,\text{mm}$, what is $\beta$?

$1.2\,\text{mm}$ ($1.2 \times 10^{-3}\,\text{m}$)

What is the round-trip geometric optical path length inside a thin film of index $n$ and thickness $t$ at normal incidence?

$$2nt$$

Why is the central spot in reflected Newton's rings typically dark?

Reflection at the lower air-glass interface introduces a $\pi$ phase shift.

How does the ring radius $r_m$ in standard reflected Newton's rings scale with order $m$?

$r_m^2 \propto m$ ($r_m^2 = m \lambda R$)

Moving one mirror in a Michelson interferometer by distance $d$ changes the optical path difference by how much?

$$2d$$

What condition specifies the first diffraction minimum for a single slit of width $a$?

$$a \sin(\theta) = \lambda$$

What equation specifies principal maxima in a diffraction grating at normal incidence?

$$d \sin(\theta) = m \lambda$$

What is Bragg's law for X-ray diffraction from crystal planes spaced by $d$?

$$2d \sin(\theta) = n \lambda$$

The phenomenon of wave polarization provides direct physical proof of what wave property?

That the wave is transverse.

What is Malus' law for the transmitted intensity $I$ through a linear polarization analyzer?

$$I = I_0 \cos^2(\theta)$$

If plane-polarized light enters an analyzer set at $60^\circ$ to its polarization axis, what fraction of intensity is transmitted?

$\frac{I_0}{4}$ ($0.25 I_0$)

What is Brewster's law for the polarizing angle $i_p$ between media of indices $n_1$ and $n_2$?

$$\tan(i_p) = \frac{n_2}{n_1}$$

At Brewster's angle, what is the angle between the reflected ray and the refracted ray?

$$90^\circ$$

Which scattering mechanism is primarily responsible for the blue color of the clear sky?

Rayleigh scattering

What is birefringence (double refraction)?

The splitting of an incident unpolarized light ray into ordinary ($o$) and extraordinary ($e$) rays inside an anisotropic crystal.

What phase retardation is introduced between orthogonal polarization components by a quarter-wave plate?

$\frac{\pi}{2}$ radians ($90^\circ$)

What phase retardation is introduced between orthogonal polarization components by a half-wave plate?

$\pi$ radians ($180^\circ$)

What fraction of unpolarized light intensity $I_0$ passes through an ideal linear polarizer?

$$\frac{I_0}{2}$$