Tru Physics

Sound Waves

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Tru Physics
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Introduction

Sound waves are mechanical waves that propagate through a medium (like air, water, or solids) as a result of vibrations, creating pressure variations that the human ear detects as sound. They are longitudinal waves, where the oscillations occur in the direction of wave propagation.

Speed of Sound

The speed of sound varies depending on the medium and its properties such as temperature, density, and pressure. For a gas, the speed of sound v_s is given by:

v_s = \sqrt{\gamma \dfrac{P}{\rho}}

where \gamma is the adiabatic index, P is the pressure, and \rho is the density of the medium.

Wave Equation

The wave equation for a sound wave propagating in one dimension is given by:

\dfrac{\partial^2 p}{\partial x^2} = \dfrac{1}{v^2} \dfrac{\partial^2 p}{\partial t^2}

where p is the pressure variation, x is the position, t is the time, and v is the speed of the wave.

Frequency and Pitch

The frequency of a sound wave determines the pitch of the sound. Higher frequencies result in higher pitches. The frequency f of a sound wave is related to its wavelength \lambda and speed v_s by:

f = \dfrac{v_s}{\lambda}

Intensity and Loudness

The intensity I of a sound wave is the power per unit area, and it determines the loudness of the sound. It is given by:

I = \dfrac{P}{A}

where P is the power and A is the area. The perceived loudness, measured in decibels (dB), is a logarithmic measure of the sound intensity.

Doppler Effect

The Doppler effect is the change in frequency or wavelength of a wave for an observer moving relative to the wave source. For sound waves, the observed frequency f' is given by:

f' = \dfrac{f (u + v_{o})}{u + v_{s}}

where f is the source frequency, u is the speed of sound, v_{o} is the speed of the observer, and v_{s} is the speed of the source. The signs in the formula depend on the direction of motion of the source and observer.

Applications

Sound waves have numerous applications, including in music, medicine (e.g., ultrasound imaging), seismology, and various technologies like sonar and echolocation. They are also crucial in the study of acoustics, the branch of physics that deals with the properties of sound.

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