Sound Intensity and Longitudinal Waves
Explore the concepts of sound intensity, energy flux, and longitudinal waves. Learn about the inverse-square law, decibel scale, and how sound intensity levels change with distance. Dive into the properties of longitudinal waves and understand particle acceleration and speed in wave oscillations.
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Presentation Transcript
Sound Intensity Energy flux at your eardrums 16.3
Sound Intensity I = (Power output)/(Area) = (Force) (Displacement velocity)/(Area) = (Force/Area) (Displacement velocity) = (Pressure) (Displacement velocity) = p(x,t) vy(x,t)
Intensity and Distance Inverse-square law: Source transmits power P At distance R, energy is spread over area A = 4 R2 Intensity at distance R is P/A P IR = 4 R2
Sound Intensity Level Decibel scale I = (10 dB) log10I0 Reference intensity I0 = 10 12 W/m2 Audibility threshold at 1000 Hz A 10-dB increase in intensity level represents a factor-of-10 increase in sound intensity
Decibel Differences I = (10 dB) log10I0 I2 2 1 = (10 dB) log10I1 R12 R22 R1 R2 = (10 dB) log10 = (20 dB) log10
Example Problem 30 m from an outdoor concert stage, the sound intensity level is 80 dB. What is the sound intensity level 40 m from the stage? 2 1 = (20 dB) log10(R1/R2) 2 = 1 + (20 dB) log10(R1/R2) = 80 dB + (20 dB) log10(30/40) = 80 dB + (20 dB) ( 0.125) = 80 dB 2.50 dB = 77.5 dB
Longitudinal Waves 16.1
Group Poll For any wave/oscillation: What is the particle acceleration when the particle speed is greatest? A. Maximum. B. Zero. C. ? What is the particle speed when the particle acceleration is greatest? A. Maximum. B. Zero. C. ?
Longitudinal Waves 0 1/8 T 2/8 T 3/8 T 4/8 T 5/8 T 6/8 T 7/8 T Where are crests and troughs? Which way is acceleration?
Board Work Draw several cycles of a longitudinal wave train. What force accelerates the particles? Identify where pressure is high or low. Identify the acceleration directions at different positions along a phase.
Group Poll For a sound wave: What is the pressure excursion where the particle acceleration is greatest? A. Maximum. B. Zero. C. ? What is the particle acceleration where the pressure excursion is greatest? A. Maximum. B. Zero. C. ?
End Result Pressure is 90 out of phase with displacement Pressure is greatest when forward velocity is greatest Pressure is least when backward velocity is greatest
