Propagation of Sound Waves

Vocabulary practice flashcards covering the production, propagation, characteristics, governing equations, medium dependencies, and comparative speeds of sound waves.

Sound

A form of mechanical energy produced by vibrating bodies that travels through a medium in the form of waves to produce the sensation of hearing in our ears.

Tuning Fork

A rectangular rod of steel or aluminium bent into a U shape with a metallic stem at the bend, used to produce sound waves through the mechanical vibrations of its prongs.

Bell Jar Experiment

A demonstration using an electric bell suspended in a glass bell jar connected to a vacuum pump, showing that sound becomes inaudible once air is completely evacuated and thus requires a material medium to propagate.

Elasticity of the Medium

A requisite property of a medium for sound propagation that ensures displaced particles are capable of returning to their initial mean positions after being disturbed.

Inertia of the Medium

A requisite property of a transmitting medium that enables its particles to store mechanical energy during wave propagation.

Compression ($C$)

A region in a longitudinal wave where the layers of the medium are pushed together, causing maximum density and maximum pressure.

Rarefaction ($R$)

A region in a longitudinal wave where the layers of the medium expand or separate, causing minimum density and minimum pressure.

Longitudinal Wave

A wave in which the particles of the medium vibrate about their mean positions parallel to the direction of propagation of the wave, capable of traveling in solids, liquids, and gases.

Transverse Wave

A wave composed of crests and troughs in which the particles of the medium vibrate perpendicular to the direction of wave propagation; it can only propagate in solids and on the surfaces of liquids.

Crest

The position of maximum upward displacement of the particles of a medium in a transverse wave.

Trough

The position of maximum downward displacement of the particles of a medium in a transverse wave.

Amplitude ($a$)

The maximum displacement of a particle of the medium on either side of its mean position as a wave passes through, measured in metres ($\text{m}$).

Time Period ($T$)

The time taken by a particle of a medium to complete one full vibration, measured in seconds ($\text{s}$).

Frequency ($f$)

The number of vibrations made by a medium particle in one second, defined by $f = \frac{1}{T}$, measured in hertz ($\text{Hz}$) or $\text{s}^{-1}$, and determined solely by the source of the disturbance.

Wavelength ($\lambda$)

The distance travelled by a wave during one time period ($T$) of vibration, equal to the separation between two consecutive compressions, rarefactions, crests, or troughs, measured in metres ($\text{m}$).

Wave Velocity ($V$)

The distance travelled by a wave per second ($V = f\lambda$), representing the speed at which energy is transferred through the medium, measured in $\text{m\,s}^{-1}$.

Displacement-Distance Graph

A graphical representation showing the instantaneous displacement of various medium particles relative to distance along the wave's path, also termed a snapshot of a wave.

Newton's Formula for Speed of Sound

The expression $V = \sqrt{\frac{P}{\rho}}$ derived under the assumption that sound propagation in a gas is an isothermal process where the elasticity modulus equals pressure ($E = P$), predicting a speed of $279.5\,\text{m\,s}^{-1}$ in air at N.T.P.

Laplace's Correction

The correction to Newton's formula stating that sound travels via an adiabatic process without heat exchange ($E = \gamma P$), giving the formula $V = \sqrt{\frac{\gamma P}{\rho}}$, yielding approximately $330.7\,\text{m\,s}^{-1}$ in air at N.T.P.

Adiabatic Ratio ($\gamma$)

The ratio of the specific heat of a gas at constant pressure to that at constant volume ($\gamma = \frac{C_p}{C_v}$), which has a value of $1.4$ for air.

Temperature Effect on Sound Speed

The direct proportionality of the speed of sound in a gas to the square root of absolute temperature ($V \propto \sqrt{T}$), increasing by approximately $0.61\,\text{m\,s}^{-1}$ for each degree Celsius rise ($V_t = V_0 + 0.61t$).

Humidity Effect on Sound Speed

The increase in the speed of sound in moist air compared to dry air, caused by the lower density of water vapour (about $\frac{5}{8}$ times the density of dry air at ordinary temperatures).

Wind Effect on Sound Speed

The variation in apparent sound speed depending on wind motion, resulting in $V + W$ when traveling with the wind and $V - W$ when traveling against the wind.

Pressure Independence of Sound Speed

The principle that changes in gas pressure do not alter the speed of sound because density varies proportionally with pressure, keeping the ratio $\frac{P}{\rho}$ constant.

Speed of Sound vs. Speed of Light

A physical comparison where light is a transverse electromagnetic wave traveling through a vacuum at $3 \times 10^8\,\text{m\,s}^{-1}$, while sound is a longitudinal mechanical wave requiring a medium and traveling at only $330\,\text{m\,s}^{-1}$ in air at $0^\circ\text{C}$.

Two-Observer Method

An experimental technique for finding the speed of sound in air by firing guns alternately between two separated stations $A$ and $B$ over a known distance $d$, using $V = \frac{2d}{t_1 + t_2}$ to eliminate errors caused by wind flow.