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**Chapter 22B: Acoustics A PowerPoint Presentation by**

Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007

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**Objectives: After completing this module, you should be able to:**

Compute intensity and intensity levels of sounds and correlate with the distance to a source. Apply the Doppler effect to predict apparent changes in frequency due to relative velocities of a source and a listener.

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Acoustics Defined Acoustics is the branch of science that deals with the physiological aspects of sound. For example, in a theater or room, an engineer is concerned with how clearly sounds can be heard or transmitted.

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Audible Sound Waves Sometimes it is useful to narrow the classification of sound to those that are audible (those that can be heard). The following definitions are used: Audible sound: Frequencies from 20 to 20,000 Hz. Infrasonic: Frequencies below the audible range. Ultrasonic: Frequencies above the audible range.

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**Comparison of Sensory Effects With Physical Measurements**

Sensory effects Physical property Loudness Pitch Quality Intensity Frequency Waveform Physical properties are measurable and repeatable.

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**Sound Intensity (Loudness)**

Sound intensity is the power transferred by a sound wave per unit area normal to the direction of wave propagation. Units: W/m2

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**Isotropic Source of Sound**

An isotropic source propagates sound in ever-increasing spherical waves as shown. The Intensity I is given by: l Intensity I decreases with the square of the distance r from the isotropic sound source.

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**Comparison of Sound Intensities**

The inverse square relationship means a sound that is twice as far away is one-fourth as intense, and one that is three times as far away is one-ninth as intense. I1 I2 r1 r2 Constant Power P

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**Example 1: A horn blows with constant power**

Example 1: A horn blows with constant power. A child 8 m away hears a sound of intensity W/m2. What is the intensity heard by his mother 20 m away? What is the power of the source? Given: I1 = 0.60 W/m2; r1 = 8 m, r2 = 20 m I2 = W/m2

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**The same result is found from:**

Example 1: (Cont.) What is the power of the source? Assume isotropic propagation. Given: I1 = 0.60 W/m2; r1 = 8 m I2 = W/m2 ; r2 = 20 m P = 7.54 W The same result is found from:

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Range of Intensities The hearing threshold is the standard minimum of intensity for audible sound. Its value I0 is: Hearing threshold: I0 = 1 x W/m2 The pain threshold is the maximum intensity Ip that the average ear can record without feeling or pain. Pain threshold: Ip = 1 W/m2

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**Intensity Level (Decibels)**

Due to the wide range of sound intensities (from 1 x W/m2 to 1 W/m2) a logarithmic scale is defined as the intensity level in decibels: Intensity level decibels (dB) where b is the intensity level of a sound whose intensity is I and I0 = 1 x W/m2.

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**Example 2: Find the intensity level of a sound whose intensity is 1 x 10-7 W/m2.**

Intensity level: b = 50 dB

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**Intensity Levels of Common Sounds.**

Leaves or whisper 20 dB 65 dB Normal conversation Subway 100 dB Jet engines dB Hearing threshold: 0 dB Pain threshold: 120 dB

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**Comparison of Two Sounds**

Often two sounds are compared by intensity levels. But remember, intensity levels are logarithmic. A sound that is 100 times as intense as another is only 20 dB larger! 20 dB, 1 x W/m2 Source A IB = 100 IA 40 dB, 1 x 10-8 W/m2 Source B

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**Difference in Intensity Levels**

Consider two sounds of intensity levels b1 and b2

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**Example 3: How much more intense is a 60 dB sound than a 30 dB sound?**

Recall definition: I2 = 1000 I1

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**Interference and Beats**

f f’ + = Beat frequency = f’ - f

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The Doppler Effect The Doppler effect refers to the apparent change in frequency of a sound when there is relative motion of the source and listener. Sound source moving with vs Apparent f0 is affected by motion. Left person hears lower f due to longer l. Right person hears a higher f due to shorter l

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**General Formula for Doppler Effect**

Definition of terms: f0 = observed frequency fs = frequency of source V = velocity of sound v0 = velocity of observer vs = velocity of source Speeds are reckoned as positive for approach and negative for recession

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**The truck is approaching; the boy is fleeing. Thus:**

Example 4: A boy on a bicycle moves north at 10 m/s. Following the boy is a truck traveling north at 30 m/s. The truck’s horn blows at a frequency of 500 Hz. What is the apparent frequency heard by the boy? Assume sound travels at 340 m/s. 30 m/s 10 m/s V = 340 m/s fs = 500 Hz The truck is approaching; the boy is fleeing. Thus: vs = +30 m/s v0 = -10 m/s

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**Example 4 (Cont.): Apply Doppler equation.**

vs = 30 m/s v0 = -10 m/s V = 340 m/s fs = 500 Hz f0 = 532 Hz

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Summary of Acoustics Acoustics is the branch of science that deals with the physiological aspects of sound. For example, in a theater or room, an engineer is concerned with how clearly sounds can be heard or transmitted. Audible sound: Frequencies from 20 to 20,000 Hz. Infrasonic: Frequencies below the audible range. Ultrasonic: Frequencies above the audible range.

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**Sensory effects Physical property**

Summary (Continued) Sensory effects Physical property Loudness Pitch Quality Intensity Frequency Waveform Measurable physical properties that determine the sensory effects of individual sounds

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Summary (Cont.) Sound intensity is the power transferred by a sound wave per unit area normal to the direction of wave propagation. Units: W/m2

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Summary (Cont.) The inverse square relationship means a sound that is twice as far away is one-fourth as intense, and one that is three times as far away is one-ninth as intense.

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**Summary of Formulas: v = fl**

Hearing threshold: I0 = 1 x W/m2 Pain threshold: Ip = 1 W/m2 v = fl Beat freq. = f’ - f

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**CONCLUSION: Chapter 22B Acoustics**

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