Oscillations and Waves — Practice Flashcards, Quiz, and Key Terms Flashcards

Front

SHM

Back

Simple harmonic motion (SHM) is oscillatory motion where the restoring force is proportional to displacement and directed toward equilibrium. It is described by $x(t)=A\cos(\omega t+\phi_0)$ and has angular frequency $\omega$ and amplitude $A$.

Front

Amplitude

Back

Amplitude $A$ is the maximum displacement of an oscillator from its equilibrium position. It determines the maximum kinetic and potential energies in SHM, with total energy proportional to $A^2$.

Front

Angular frequency

Back

Angular frequency $\omega$ measures how quickly the phase of an oscillator advances in radians per second. For a mass-spring system $\omega=\sqrt{\frac{k}{m}}$ and it relates to frequency via $f=\frac{\omega}{2\pi}$.

Front

Period

Back

The period $T$ is the time for one complete oscillation and is given by $T=\frac{2\pi}{\omega}$. It is the reciprocal of the frequency: $T=\frac{1}{f}$.

Front

Maximum speed (SHM)

Back

The maximum speed of a particle in SHM is $v_{\text{max}}=\omega A$. This occurs as the mass passes through equilibrium when kinetic energy is maximal.

Front

Damping

Back

Damping introduces a velocity-dependent force (e.g., $-b\dot{x}$) that reduces amplitude over time. For light damping the envelope decays as $e^{-t/\tau}$ with $\tau=\frac{2m}{b}$; if $b$ exceeds a critical $b_c$ the motion is overdamped and oscillations cease.

Front

Resonance

Back

Resonance is the large amplitude response of a driven oscillator when the driving frequency approaches the system's natural frequency. In steady state, amplitude peaks near $\omega_0$ and internal losses balance driving power.

Front

Transverse wave

Back

In a transverse wave the medium's particles oscillate perpendicular to the direction the wave travels. Examples include waves on a string and many electromagnetic waves in free space.

Front

Longitudinal wave

Back

A longitudinal wave has particle motion parallel to the wave propagation direction, producing compressions and rarefactions. Sound in air is a common longitudinal wave.

Front

Wavefunction

Back

A traveling wave can be written as $D(x,t)=f(x- vt)$ for rightward motion or $D(x,t)=A\sin(kx-\omega t+\phi_0)$ for a sinusoid. The function encodes spatial profile and time evolution of the disturbance.

Front

Wave speed on a string

Back

The speed of transverse waves on a stretched string is $v=\sqrt{\frac{T_s}{\mu}}$, where $T_s$ is tension and $\mu$ is linear mass density. This speed is a property of the medium and tension.

Front

Wavelength and frequency relation

Back

Wavelength $\lambda$, frequency $f$, angular frequency $\omega$, and wavenumber $k$ satisfy $v=\lambda f=\frac{\omega}{k}$. Changing medium may change $v$ and $\lambda$ while $f$ remains constant.

Front

Standing wave

Back

A standing wave results from the superposition of two equal traveling waves moving in opposite directions, producing nodes and antinodes. Its form can be $D(x,t)=2A\sin(kx)\cos(\omega t)$ and the nodes are spaced by $\lambda/2$.

Front

Nodes and antinodes

Back

Nodes are positions of zero amplitude in a standing wave and remain stationary; antinodes are positions of maximum oscillation. Nodes occur at $x_m=\frac{m\lambda}{2}$ for integer $m$.

Front

Normal modes

Back

Normal modes of a string are standing-wave patterns with frequencies $f_m= m f_1$ and wavelengths $\lambda_m=\frac{2L}{m}$, where $m$ is a positive integer. The fundamental ($m=1$) has the lowest frequency.

Front

Open vs closed pipes

Back

A tube open at both ends supports wavelengths $\lambda_m=\frac{2L}{m}$ with $m=1,2,3,\dots$, while a tube open at one end only supports odd harmonics $\lambda_k=\frac{4L}{k}$ with $k=1,3,5,\dots$. This changes the allowed resonant frequencies.

Front

Doppler effect

Back

The Doppler effect is the observed shift in frequency when source or observer moves relative to the medium. For a moving source with speed $v_s$, the detected frequency is $f'=\frac{f_0}{1- v_s/v}$ for approach and $f'=\frac{f_0}{1+ v_s/v}$ for recession (observer at rest).

Front

Beats

Back

Beats result when two waves of similar frequency superpose, producing amplitude modulation at the beat frequency $f_{\text{beat}}=|f_1-f_2|$. The audible beat frequency equals the difference between the component frequencies.