Sound

Consider a vibrating tuning fork.

As the tines of the tuning fork vibrate back and forth they will alternately produce regions of high density air and low density air. These compressions and rarefactions will propagate away from the tuning fork. The individual molecules of the material through which the wave is propagating will oscillate in a direction parallel to the direction of propagation. Thus, sound is a longitudinal wave. Sound can be represented by a harmonic wave. The displacement from equilibrium is sinusoidal. In addition, the pressure can also be represented as a sinusoidal function. A crest in the pressure wave corresponds to a region of compression, a trough in the pressure wave corresponds to a region of rarefaction.

• How fast will the waves move?
• depends on the elastic properties of the medium
• depends on the inertial properties of the medium
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• The speed of sound is also temperature dependent
• for a sound wave traveling through air
• (T in degrees Celsius)
• Describing the sound wave
• segment of air oscillating with simple harmonic motion
• let s be the displacement of the element of air away from equilibrium
• 
• similar to expression for transverse wave
• omega, k, lambda, and f are found in the same way as for transverse
• lambda measures distance between maximum regions of compression
• As the density of the air changes, the pressure must also change.
• We know the density and the change in volume are related by
• or



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• Substituting the above two equations into the previous expression



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• the derivative of s with respect to x (while keeping t constant)



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• Loudness
• Intensity (I) [W/m²]
• average rate per unit area at which energy is transmitted by the wave
• consider a section of air vibrating back and forth
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• The power is the rate at which energy is transferred
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• and the intensity is the power per unit area



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• Measuring the Intensity
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• I₀ = threshold of hearing = 1 x 10^-12 W/m²