1. 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

2. Transverse vs. Longitudinal Waves I
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 Waves II
Transverse vs. longitudinal waves on slinky
Transverse
Longitudinal

4. Transverse vs. Longitudinal Waves III
Sound - Pressure wave vs. velocity wave

5. 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≈ 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. 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 𝜋 𝑟 1 2
𝐼 2 𝐼 1 = 𝑟 𝑟 2 2
General Rule: Inverse square law

12. Intensity/Amplitude variation with distance
𝐼 2 𝐼 1 = 𝑟 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 𝑘𝑚 𝑘𝑚 2 = 𝐼 1

13. 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

14. 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