Sound and Intensity Transverse vs. Longitudinal Waves Sound Frequency Sound Loudness Loudness and the Decibel Scale db Examples Intensity decrease with distance Other db scales

Transverse vs. Longitudinal Waves I String (transverse) wave animation https://sites.google.com/site/physicsflash/home/transverse Air (longitudinal) wave animation https://sites.google.com/site/physicsflash/home/sound Wavelength – distance between peaks at fixed time Frequency – time between repetitions at fixed position Velocity from wavelength and frequency 𝑣=𝑓𝜆

Transverse vs. Longitudinal Waves II Transverse vs. longitudinal waves on slinky http://www.animations.physics.unsw.edu.au/jw/sound-pressure-density.htm Transverse Longitudinal

Transverse vs. Longitudinal Waves III http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/long_wave.html Sound - Pressure wave vs. velocity wave

Waves on string vs waves in air Both have Wavelength – distance between peaks at fixed time Frequency – rate of repetitions at fixed position (like your ear) Wave velocity 𝑣=𝑓𝜆 Differences String wave velocity varies with tension and mass/length 𝑣= 𝑇 𝜇 Air wave velocity set at 343 m/s (at 20° C) * *at any temperature 𝑣≈ 331+0.60𝑇 𝑚 𝑠 )

Frequency (pitch) of Sound Waves http://www.animations.physics.unsw.edu.au/jw/sound-pitch-loudness-timbre.htm http://www.animations.physics.unsw.edu.au/jw/frequency-pitch-sound.htm Human ear ~ 20 Hz to 20,000 Hz (dogs higher)

Loudness (volume) of Sound Waves http://www.animations.physics.unsw.edu.au/jw/sound-pitch-loudness-timbre.htm Human ear can hear from about 10-12 W/m2 to 100 W/m2 - about 14 orders of magnitude!

Intensity and decibel scale Range of human ear Intensity 10-12 – 100 watts/m2 Make scale more convenient - “compress” this Try Logarithms log 10 𝑥 =𝑥⁡ Method 3 gives most convenient scale Definition decibel (sound) 𝛽 𝑑𝑏 =10 𝑙𝑜𝑔 𝐼 10 −12 Method Intensity Log Log(I) 𝐼= 10 −12 → 10 2 𝐿𝑜𝑔 𝐼 = −12 → +2 Log(I/10-12) 𝐿𝑜𝑔 𝐼 10 −12 = 0 → 14 10 Log(I/10-12) 10 𝐿𝑜𝑔 𝐼 10 −12 =0 →140

Example - Intensity and db scale Auto interior sound intensity 3 x 10-5 W/m2. What is decibel level? 𝛽=10 𝑙𝑜𝑔 3∙ 10 −5 10 −12 =10 𝑙𝑜𝑔 3∙ 10 7 (use calculator) =10∙7.477≈75 𝑑𝑏 (fractional logarithms OK) The sound level for a jet plane at takeoff is 140 db. What is the intensity? 10 𝑙𝑜𝑔 𝐼 10 −12 =140 → 𝑙𝑜𝑔 𝐼 10 −12 =14 𝐼 10 −12 = 10 14 → 𝐼= 10 2 =100 𝑊 𝑚 2 ( 10 𝑙𝑜𝑔 𝑥 =𝑥) Logarithm rules on textbook inside back cover

Example 12-4 – Loudspeaker volume 3 db Intensity difference 10 𝑙𝑜𝑔 𝐼 2 10 −12 −10 𝑙𝑜𝑔 𝐼 1 10 −12 = 𝛽 2 − 𝛽 1 =3𝑑𝑏 10 𝑙𝑜𝑔 𝐼 2 𝐼 1 =3 (difference/quotient rule) 𝑙𝑜𝑔 𝐼 2 𝐼 1 =0.3 𝐼 2 𝐼 1 = 10 0.3 =2 𝐼 2 =2 𝐼 1

Energy spreading in spherical wave Intensity defined 𝐼= 𝑃𝑜𝑤𝑒𝑟 𝐴𝑟𝑒𝑎 For wave spreading over sphere 𝐼= 𝑃𝑜𝑤𝑒𝑟 4𝜋 𝑟 2 Ratio at 2 distances 𝐼 2 𝐼 1 = 1 4𝜋 𝑟 2 2 1 4𝜋 𝑟 1 2 𝐼 2 𝐼 1 = 𝑟 1 2 𝑟 2 2 General Rule: Inverse square law

Intensity/Amplitude variation with distance 𝐼 2 𝐼 1 = 𝑟 1 2 𝑟 2 2 Amplitude 𝐼∝ 𝐴 2 𝐼 2 𝐼 1 = 𝑟 1 𝑟 2 Example Earthquake power 106 W/m2 at 100 km, what is it at 400 km? 𝐼 2 = 𝐼 1 100 𝑘𝑚 2 400 𝑘𝑚 2 = 1 16 𝐼 1

Example 12-5 – Airplane roar Translate 140 db at 30 m to intensity 10 𝑙𝑜𝑔 𝐼 1 10 −12 =140 𝐼 1 10 −12 = 10 14 𝐼 1 =100 𝑊 Scale from 30 m to 300 m using inverse square law 𝐼 2 = 𝐼 1 𝑟 1 𝑟 2 2 =100 𝑊 1 100 =1 𝑊 Translate at 300 m back to db 𝛽=10 𝑙𝑜𝑔 1 10 −12 =120 𝑑𝑏

FYI - Other “Decibel” scales Sound db - referenced to 10-12 W. 𝛽=10 𝑙𝑜𝑔 𝐼 10 −12 Electrical dbm - referenced to 10-3 W. 𝛽 𝑑𝑏𝑚 =10 𝑙𝑜𝑔 𝐼 10 −3 2G/3G/4G/WIFI signal strengths (WIFI > -20 dbm near router.) Comcast checks cable modem this way. db always log of power ratio to some reference power. Cellphone signal strengths