PHY2053 Lecture 27 - University of Florida...PHY2053, Lecture 4, Motion in a Plane Amplitude and intensity of sound • human register sound 13 orders of magnitude in intensity between

PHY2053 Lecture 27 Ch. 12.1 - 12.5: Sound Waves, Amplitude, Intensity

PHY2053, Lecture 4, Motion in a Plane

Sound

• periodic variation of pressure - pressure waves• propagate through any material - gas, fluid or solid• compressions - areas of higher pressure• rarefactions - areas of lower pressure• sound source - object which oscillates within audible

range of frequencies• movement translates into pressure waves• pressure waves detected by eardrums (vibration)• audible range: 20 Hz to 20 kHz• infrasound - below 20 Hz, ultrasound - above 20 kHz

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Speed of sound waves• last lecture - dimensions of resonating system

determine wavelength, v = f × λ• transverse wave on a string:

• F - measure of restoring force• μ - measure of inertia of the system

• analogy for fluids:

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Bulk Modulus

Density


Speed of sound in gas and solids• for a gas, the bulk modulus is either the pressure (p)

(isothermal) or γp (adiabatic)

• temperature dependence:

• speed of sound along the length of a thin solid rod:

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Young’s Modulus

Density


Example problem:Dolphins emit ultrasonic waves with a frequency as high as 2.5 ×105 Hz. What is the wavelength of such a wave in seawater at 25 ºC? [the speed of sound in water at 0 ºC is 1493 m/s]

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p0 = !v⇢s0

I =p202⇢v

I ⇠ amplitude2


Amplitude and intensity of sound

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Pressure amplitude Osc. object amplitude

mass density of mediumspeed of sound in medium

sound frequency


Amplitude and intensity of sound• human register sound 13 orders of magnitude in

intensity between lowest intensity and pain threshold• if lowest intensity is 1, pain is 10 000 000 000 000• lowest sound intensity I0 = 10-12 W/m2

• ear registers intensity in orders of magnitude• intensity increase from 1 to 10 appears equivalent to

intensity increase from 10 to 100• a logarithmic scale is most appropriate, measure

sound intensity in decibels:

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Example problemThe amplitude of oscillation of a loud speaker is increased by 50%.a) By what percentage does the intensity increase?b) What is the change in intensity level (in dB)?

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Example problemThe amplitude of oscillation of a loud speaker is increased by 50%.a) By what percentage does the intensity increase?b) What is the change in intensity level (in dB)?

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Solution, continued

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PHY2053, Lecture 26, Interference and Diffraction

Standing Sound Waves• reminder from last time:• what happens when a standing wave gets “trapped”

between two boundaries? • superposition of incoming and reflected wave, while

taking into account boundary conditions• for example two fixed ends:

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Unusual (but possible) Configuration

• one fixed end, one free end:

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Example Problem• How long of a pipe is needed to have the lowest

resonant frequency of 440 Hz [pitch standard] ? Assume the pipe is open at both ends.

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H-ITT from last lecture

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Timbre• no instrument produces only one harmonic• sounds produced are a superposition of harmonics• timbre / tone quality / tone color - spectrum of

harmonics specific to a particular instrument

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Timbre, continued

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Timbre, continued

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Timbre, continued

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Timbre, continued

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PHY2053 Lecture 27 - University of Florida...PHY2053, Lecture 4, Motion in a Plane Amplitude and intensity of sound • human register sound 13 orders of magnitude in intensity between