Sound Intensity

Sound Intensity & sonic boom

5-1. Did you read > 70% of 17: 1-4? A. Yes B. No Today: new symbols B, I, β last chapter : wave equation, power α Amplitude2 ∂ The concepts: 1. sound intensity ≡ power/area; I ≡ P/A 2. how to do problems with decibels inverse square-of-distance relationship 3. Sound & pressure

No student assigned to these transmitter #s on Friday. (Anyone need a name label for it?)

01103021 0C888206 16D75998 1B0E5144 1B44104F 1DBF07A5 1E505C12

08F58B76 1615BFBC 16D965AA 1B3E85A0 1B4B6C3C 1DC7DC06 025AE9B1

The Handout.

►

Remember: the online schedule has precedence.

Velocity, pressure & intensity • V= √(B/ρ), where B is bulk modulus. • Pressure is 90° (π/2) out of phase with displacement. • Decibels. β = 10 log(I/Io)

Pressure is 90° (π/2) out of phase with displacement. We will talk more about now to read these graphs later.

But look at the brown curve maxima & the gas in the tube.

5-2 What are the units of intensity?

A.energy B.power C.energy/area D.power/area E.power/volume

Sound Speed in Solids, Liquids, and Gases:

v=

B

ρ

, = v

( 331 m s )

1 + T 273°C

Power, Intensity, and Loudness:

I=

Ρ av 4π r 2

, I1 r22 = I 2 r12 ,

β = 10 log10 ; I=A2

I Io

Intensity energy passing thru an area in unit time.

As we get closer to the fronts What is a wave front?

Decibels & Intensity • Experiments on human hearing have shown that we hear intensity differences logarithmically, so the decibel loudness scale for sound intensity was invented. The loudness β of a sound in decibels is related to its intensity I in W/m2 by the formula

β ≡ 10 log I/Io or I = Io10^(β/10) • Where Io is a sound intensity near the threshold of hearing, defined to be Io = 10-12 W/m2. Note that on this scale, a sound is made 10 times more intense by adding 10 decibels. 120 db threshold of pain. 1 W/m2.

Examples • If I= 10,000 times the threshold, then the ratio of the intensity to the threshold intensity is 104, the power of ten is 4, and the intensity is 40 dB. • This also works for ratios, so if I is 10,000 times a whisper (30 dB) then the sound will be _____dB.

5-3. What factor has the intensity increased for a 20dB change? pp

A. B. C. D.

10 20 100 not at all

Look at some intensities.

Pressure Amplitude & Intensity • Intensity α Amplitude2 • Zero dB is displacement of 10 -11 m. • 120 dB is displacement amplitude of 10 μm ; 30 Pa or 3 mm of water.

Inverse square-of-distance Law • For sound moving out of a point source. •

•

I =P /A 2 =P/(4πr ) -2 thus I α r ; I1/ I2 = (r2/r1)2

5-4 Part. point. At 1m 80 dB. How far from the radio should I sit to get 60 dB?

A.3 m B.10 m C.30 m D.100 m E.> 300 m

Thought question: At 1m 80 dB. How far from the radio should I sit to get 0 dB?

A.3 km B.10 km C.30 km D.100 km E.> 300 km

Why can’t you hear a radio from LV, NV in Provo?

Sonic Booms

Ripple tank to understand waves

Decibels • The sound intensity I may be expressed in decibels above the standard threshold of hearing I0 . The expression is • • The logarithm involved is just the power of ten of the sound intensity expressed as a multiple of the threshold of hearing intensity. Example: If I= 10,000 times the threshold, then the ratio of the intensity to the threshold intensity is 104, the power of ten is 4, and the intensity is 40 dB: •

• • • • • •

The factor of 10 multiplying the logarithm makes it decibels instead of Bels, and is included because about 1 decibel is the just noticeable difference (JND) in sound intensity for the normal human ear. Decibels provide a relative measure of sound intensity. The unit is based on powers of 10 to give a manageable range of numbers to encompass the wide range of the human hearing response, from the standard threshold of hearing at 1000 Hz to the threshold of pain at some ten trillion times that intensity. Another consideration which prompts the use of powers of 10 for sound measurement is the rule of thumb for loudness: it takes about 10 times the intensity to sound twice as loud. Decibel calculationDynamic levels of music in dB Index Sound level measurement HyperPhysics***** Sound R NaveGo Back

• • • • • • •

Decibels and Logarithms The decibel scale is a reflection of the logarithmic response of the human ear to changes in sound intensity:

•

Index

The logarithm to the base 10 used in this expression is just the power of 10 of the quantity in brackets according to the basic definition of the logarithm: Examples: Decibel calculation

Sound level measurement HyperPhysics***** Sound R NaveGo Back

• • • • • • • • •

Decibel Calculation The sound intensity in decibels above the standard threshold of hearing is calculated as a logarithm. If the intensity as a multiple of threshold is = x 10^ then the intensity in decibels is given by Decibels can also be used to express the relative intensity of two sounds. If one is expressed as a multiple of the other: IA = xIB = x 10^xIB then the difference in decibels is given by IA = dB above IB