SounSoundd

AP Physics: M. BlachlyAP Physics: M. Blachly

Nature of Sound Wave

Sound is a mechanical, longitudinal, pressure wave.

Nature of Sound Wave

What, exactly, is oscillating?

Air molecules are compressed together by the mechanical motion of some solid matter.The compressions and rarefactions propagate through the medium

Terminology

Compressions are areas of increased molecular density

Rarefactions are regions of decreased density

Pressure Graph

Speed of Sound

Bulk modulus

fluids

Bv

B

05

Medium Speed (m/s)

Air 343

Helium 972

Water 1500

Steel 5600

string

Fv

Recall that the bulk modulus is the ratio of the stress to the strain. It is an effective “spring constant” for the fluid

TnR

How would you expect the speed of sound in air (v) to depend on the temperature (T) of the air?

• 1. v will increase as T increases

• 2. v will decrease as T increases

• 3. v will not depend on T

Temperature Dependence

As the air heats up, the molecules move faster and the pressure wave passes through the medium faster.

The functional relationship is given by the empirical formula:

331 m/s 1273

Tv

Paint Bomb

Suppose a paint bomb exploded. How would the thickness of the paint on your face depend on how far you were from the bomb?

Energy and Intensity

Waves transmit energy

The rate that energy is transmitted is the power.

What is intensity?

Intensity is the “concentration” of power on a particular area

Intensity is the rate at which energy flows to a given area, perpendicular to the direction of wave travel.

power

area

PI

A 2

WattsUnits:

m

Example of Spherical Waves

Assume that a 100 W speaker radiates energy outwards in a sphere. What is the intensity of this sound a distance of 3 meters from the source.

2

2

2

4

4

0.884 W/m

A r

P PI

A r

I

Intensity TnRRecall Intensity = P/A. If you are standing 6 meters from a speaker, and you walk towards it until you are 3 meters away, by what factor has the intensity of the sound increased?

A: 2

B: 4

C: 8

D: ½

E: ¼

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Graph This Data:

Source Intensity

Gentle Breeze 1E-11 W/m2

Whisper 5E-9 W/m2

Conversation 2E-6 W/m2

Orchestra 6E-3 W/m2

iPod on Max w/ earbuds 0.02 W/m2

F-16 at Takeoff 100 W/m2

Your Ear

Your Ear is sensitive to an amazing range! (1dB – 100 dB)

• Lowest limit: 10-12 Watts/m2

• Upper limit: 1 Watt/m2

Like a laptop that can run using all power of

• A single battery

• Entire Nuclear Power Plant

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The Ear

We (humans) do not have a linear response to sound.

When the intensity doubles, we do not register that the sound is twice as loud.

Our response is actually more logarithmic

It makes sense then to define an intensity scale that is more matched to what we experience

Intensity Scale

Intensity scale is a log scale, called the decibel scale.

It measures the intensity relative to a reference level, known as the threshold of hearing.

Io = 1 x 10-12 W/m2.

10logo

I

I

Examples

A speaker emits 600 Joules of energy each second. Assuming a spherical wave, calculate the intensity (in decibels) a distance of 5 meters away from the source.

= 122.8 dB

Find the power of a source if the intensity at a distance of 120 meters is 65 dB.

The Decibel Scale

Source

Threshold of Hearing 1x10-12 W/m2 0 dB

Rustling Leaves 1x10-11 W/m2 10 dB

Whisper 1x10-10 W/m2 20 dB

Normal Conversation 1x10-6 W/m2 60 dB

Busy Street Traffic 1x10-5 W/m2 70 dB

Vacuum Cleaner 1x10-4 W/m2 80 dB

Large Orchestra 6.3x10-3 W/m2 98 dB

iPod on Loud 1x10-2 W/m2 100 dB

Front Row, Concert 1x10-1 W/m2 110 dB

Threshold of Pain 1x101 W/m2 130 dB

Military Jet Takeoff 1x102 W/m2 140 dBPerforation of Eardrum 1x104 W/m2 160 dB

Intensity

Example Problem #1

A sound wave has an intensity of 0.0533 W/m2. What is the intensity of this sound in db?

A pair of headphones reduce the noice level by 25db. What intensity would reach your ears if you were wearing these headphones?

Example Problem #2

A loud, obnoxious student at a swim meet (let’s call him Ryan*) can produce a sound level of 90 db at a distance of 2 meters.

Find the intensity of this wave.

What power is required to produce this wave, assuming that it is spherically distributed.

*Note: this is a hypothetical student and any resemblance to any actual student you may or may not know is purely coincidental.

TnR

As a police car passes you with its siren on, the frequency of the sound you hear from its siren

1) Increases 2) Decreases 3) Same

Doppler Example Audio

Doppler Example Visual

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Doppler Effect, moving source

When source is coming toward you (vs > 0)

• Distance between waves decreases

• Frequency increases

When source is going away from you (vs < 0)

• Distance between waves increases

• Frequency decreases

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Doppler Effect , moving observer

When moving toward source (vo < 0)

• Time between waves peaks decreases

• Frequency increases

When away from source (vo > 0)

• Time between waves peaks increases

• Frequency decreases

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Doppler Effect, combined

0

velocity of source

velocity of observer

velocity of sound

o

s

s

v vf f

v v

v

v

v

Doppler TnR

A: You are driving along the highway at 65 mph, and behind you a police car, also traveling at 65 mph, has its siren turned on.

B: You and the police car have both pulled over to the side of the road, but the siren is still turned on.

In which case does the frequency of the siren seem higher to you?

1. Case A

2. Case B

3. same correct

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Sonic Effects

What if vs > v ?

Sonic Boom

When the velocity is greater than the speed of sound, the pressure waves build up along a cone that trails the source.

Mach = velocity of source / velocity of soundVisualizations: http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=21