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

2. 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

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

4. Transverse vs. Longitudinal Comparison
Transverse vs. Longitudinal Waves

5. 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 )

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

7. Loudness (volume) of Sound Waves
Human ear can hear from about
10-12 W/m2 to 100 W/m2 -
about 14 orders of magnitude!

8. 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

9. 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

10. 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

11. 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

12. 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