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Understanding Pressure Waves and Sound Intensity: The Relationship Between Decibels and Loudness

This text delves into pressure waves, also known as longitudinal waves, exploring how pressure is measured against displacement. It explains concepts of compression and rarefaction, highlighting phase differences between pressure and displacement waves. Additionally, the intensity of sound is discussed, including its measurement in decibels and the relationship between intensity and perceived loudness. Important principles like the logarithmic scale of decibels are clarified, detailing how sound intensity influences loudness perceptions, including the human ear's sensitivity to various sound levels.

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Understanding Pressure Waves and Sound Intensity: The Relationship Between Decibels and Loudness

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  1. Sound Part 2

  2. Pressure Waves • a.k.a. longitudinal waves • Pressure is easier to measure than displacement • Compression- pressure is higher since molecules are closer together • Rarefaction- pressure is less than normal since molecules are farther apart than normal • note that the displacement wave is 1/4 λout of phase with the pressure wave

  3. Pressure Waves When pressure is a max. or min., displacement from equilibrium position is zero When pressure variation is zero, displacement is at a max. or min.

  4. Intensity of Sound: Decibels • Loudness- relates to intensity or energy transported per unit time acrossunit area. • I ∝ A2 and E/t = Power • Therefore I is measured in W/m2 • Human ear- 10-12W/m2 to 1 W/m2 • More than the one W/m2 and you feel pain!

  5. Intensity of Sound: Decibels • Producing a sound twice as loud requires a sound wave with 10x the intensity • 10-2W/m2 sounds twice as loud as 10-3 W/m2 and four times as loud as 10-4 W/m2 • Alogarithmic scale is needed to compare loudness easily

  6. Intensity of Sound: Decibels • Bel - the unit of the logarithmic scale used to compare loudness • Named after Alexander Graham Bell • Decibel - 1/10th of a Bel(10 dB = 1 Bel) • Intensity:

  7. Intensity of Sound: Decibels • Io= 1x 10-12W/m2, the threshold for human hearing • So, for a sound with an intensity = 1 x 10-10W/m2

  8. Intensity of Sound: Decibels • An increase in intensity by a factor of • 10 means a level increase of 10 dB • 100 means a level increase of 20 dB • A50 dB sound is 100 times more intense than a 30 dB sound

  9. Intensity of Sound: Decibels

  10. Intensity of Sound: Decibels • A sound level difference of 3 dB (twice the intensity) corresponds to a very small change in the subjective sensation of apparent loudness. • Loudness decreases as you get farther from the source • I ∝ (1/r2)

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