Physics
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Sound Waves: Nature and Propagation
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⚡ Quick Summary
Sound waves are created by vibrating sources that compress and rarefy the medium, creating pressure variations that propagate as waves. These waves consist of alternating compressions (high pressure) and rarefactions (low pressure). The speed of the wave depends on the medium's properties. Human hearing is limited to frequencies between 20 Hz and 20,000 Hz.
['δP = P - P₀ = δP₀ sin ωt (Excess pressure as a function of time at the source)', 'δP = δP₀ sin ω(t - x/v) (Excess pressure at position x and time t)', 'p = p₀ sin ω(t - x/v) (Wave equation for excess pressure)', 'ν = ω / (2π) (Frequency of the wave)']
- Sound is produced by vibrating sources in a material medium.
- The vibrating source compresses the medium, increasing density locally, then rarefies it as it moves back.
- Compressions and rarefactions travel through the medium at a speed dependent on its elastic and inertial properties.
- A vibrating tuning fork creates a series of compressions and rarefactions. When the prong moves forward, it creates a compression; when it moves backward, it creates a rarefaction.
- The pressure variations caused by the vibrating source can be described as a simple harmonic motion.
- The excess pressure at any point x at any time t can be represented as: δP = δP₀ sin ω(t - x/v), where δP is the excess pressure, δP₀ is the maximum excess pressure, ω is the angular frequency, t is time, x is position, and v is the wave speed.
- Sound waves consist of alternate compression and rarefaction pulses.
- Audible sound frequency range for humans is approximately 20 Hz to 20,000 Hz.
Sound Waves
11
⚡ Quick Summary
Sound waves are longitudinal waves caused by compressions and rarefactions in a medium. They have frequencies that determine whether they are audible, infrasonic, or ultrasonic. Wavefronts represent points of equal phase and can be spherical or planar.
v = nλ
s = s₀ sin(ωt - x/v)
Infrasonic Waves: Waves with frequency below the audible range.
Ultrasonic Waves: Waves with frequency above the audible range.
Wavefront: The surface through the points, having the same phase of disturbance.
For a homogeneous and isotropic medium, the wavefronts are normal to the direction of propagation.
Spherical Wave: For a point source placed in a homogeneous and isotropic medium, the wavefronts are spherical.
Plane Waves: If sound is produced by vibrating a large plane sheet, the disturbance produced in front of the sheet will have the same phase on a plane parallel to the sheet. The wavefronts are then planes and the direction of propagation is perpendicular to these planes.
Displacement Wave: A longitudinal wave in a fluid can be described in terms of the longitudinal displacement (s) suffered by the particles of the medium. s = s₀ sin(ωt - x/v)