 Sound and Intensity Transverse vs. Longitudinal Waves Sound Frequency

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

Transverse vs. Longitudinal Waves
String (transverse) wave animation Air (longitudinal) wave animation Wavelength – distance between peaks at fixed time Frequency – time between repetitions at fixed position Velocity from wavelength and frequency 𝑣=𝑓𝜆

Transverse vs. Longitudinal Slinky
Transverse vs. longitudinal waves Transverse Longitudinal

Transverse vs. Longitudinal Comparison
Transverse vs. Longitudinal Waves

Comparison of waves on string and 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≈ 𝑇 𝑚 𝑠 )

Frequency (pitch) of sound waves
Human ear ~ 20 Hz to 20,000 Hz (dogs higher)

Loudness (volume) of Sound Waves
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 – 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 − −12 =10 𝑙𝑜𝑔 3∙ (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 = → 𝑙𝑜𝑔 𝐼 10 −12 =14 𝐼 10 −12 = → 𝐼= 10 2 =100 𝑊 𝑚 ( 10 𝑙𝑜𝑔 𝑥 =𝑥) Logarithm rules on textbook inside back cover

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

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

FYI - Other “Decibel” scales
Sound db - referenced to 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

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