Speed of sound

Problem During a thunderstorm, lightning strikes 300 m away. If the air temp is 25 Celsius, how much time passes between when you see the lightning and hear the thunder?

Doppler Effect A Doppler effect is experienced whenever there is relative motion between a source of waves and an observer. When the source and the observer are moving toward each other, the observer hears a higher frequency

When the source and the observer are moving away from each other, the observer hears a lower frequency

Motion together = higher frequency. Motion away = lower frequency.

All waves do this. Including light.

For a stationary source,a compression reaches the observer once a period.

If the source moves, eachcompression has less distanceto travel, so it takes less time to get there, so the frequencyis higher to the observer.

Moving Source.

Moving Source Behind the truck the opposite happens.

Each wave starts out from farther away, has more distance to travel, takes more time.

So, the observed frequency is lower.

Doppler Effect, (Observer Toward Source) An observer is moving toward a stationary source.

Due to his movement, the observer crosses crests more often.

The frequency heard is increased

Doppler Effect, Case 1(Observer Away from Source) An observer is moving away from a stationary source

The observer crosses fewer crests per second

The frequency appears lower

s

o

so vv

vvff

Equation for the doppler effect

fo = observed frequency

fs = source frequency

v = speed of sound

vo = observer velocity

vs = source velocity

vo – positive if moving towards each other

vs – positive if moving away from each other

A high-speed train is traveling at a speed of 44.7 m/s when the engineer sounds the 415-Hz warning horn. The speed of sound is 343 m/s. What are the frequency and wavelength of the sound, as perceived by a personstanding at the crossing, when the train is (a) approaching and (b) leaving the crossing?

s

o

so vv

vvff

A problem.

Question What happens to this equation when the object is moving towards you at the speed of sound?

s

o

so vv

vvff

Shock Waves A shock wave results when the source velocity exceeds the speed of the wave itself

The circles represent the wave fronts emitted by the source

Shock waves. The wave frontis the edge of the cone made up of the circles.

Shock Waves, cont Mach number – velocity /speed of sound

Shock Waves, cont Mach number – velocity /speed of sound

Also, sin θ = 1/Mach Number

Shock Waves, final Sonic Boom Video

http://www.youtube.com/watch?v=-d9A2oq1N38&feature=related

http://en.wikipedia.org/wiki/Chuck_Yeager

http://en.wikipedia.org/wiki/File:Bell_X-1_color.jpg

http://space.about.com/b/2004/02/20/john-glenn-first-american-to-orbit-earth.htm

Transition: New Subject

New Symbol “I” – Intensity

One description of the loudness of a noise.

Measured in Watts/meter2

Sound Intensities Threshold of hearing (I0)

Faintest sound most humans can hear Add to WOD: Faintest: 1 x 10-12 W/m2

Threshold of pain Loudest sound most humans can tolerate Add to WOD: Loudest (Tolerate): About 1 W/m2

New Symbol Decibels (dB) “β“ – beta – decibel level of sound.

A much more common measure of “loudness”

Measured in decibels (dB)

Intensity Level of Sound Waves

Add above equation to decibel WOD:

10 log

o

II

Remember logarithms? Every number can be rewritten as10something .

That’s what a log is. 100 = 102 so log 100 = 2 .1 = 10-1 so log .1 = -1 32 = 101.505 so log 32 = 1.505

Log tricks Log 1 = 0.

Log (A*B) = Log (A) + Log (B)

Log (A/B) = Log (A) – Log(B)

Intensity Level of Sound Waves

Plug in some values for I If I = I0, β = 0. Lowest “hearable” sound.

10 log

o

II

Last note on dB scale dB is a logarithmic scale. 10 x as much noise doesn’t multiply dBs by ten. It adds 10 dB to existing level.

Double dB is not Double Frequency.50dB to 100dB is not double sound loudness.50 to 60 is x10, 60 to 70 is x10,70 to 80 is x10, 80 to 90 is x10,90 to 100 is x10. So 50 to 100 is x10x10x10x10x10= x100,00050 to 100 is x100,000, NOT double.

Problem

What is the decibel level of the lowest “hearable” noise?

What is the decibel level of the threshold of pain?

10 log

o

II