Course:PHYS341/2018/Calendar/Lecture 10

Phys341 Lecture 10: Summary and web references

2018.01.24

Textbook: 9.2-9.6 (minus the math)

Slide List

1. Sound intensity
   • Sound power is the sound energy emitted in unit time
   • Normally measured in watts (W - joules per second)
   • What matters more for detection and hearing is the intensity, the power incident on a unit area
   • Which is why sound appear quieter the further you get from the source; the sound power is spread over a larger area (and may also get absorbed by intervening walls etc.)
   • Normally measured in W/m²
   • We can hear an enormous range of sound intensities (dynamic range) without discomfort
   • In the middle of the audio frequency range (~ 1 kHz) we can easily hear (but seldom experience) a billionth (10^-9) of a W/m²
   • 1 W/m² is usually considered to be at the threshold of pain
2. Intensity in English, music and physics
3. The decibel scale
4. The effect of distance on sound level
   • The way distance affects sound level is generally complicated unless the sound is radiating from a small source into an open space, in which case:
   • Double the distance, sound level drops 6 dB
   • e.g. a siren in an open field produces a SPL of 90 dB at 10 m, 84 dB at 20 m, 78 dB at 40 m etc.
   • If you want to see the math, its all in chapter 9 of Physics and Music
   • This is an example of physicists’ beloved inverse square law but is seldom observed in the real world, because of:
   • Inside: reflections and absorption due to walls, ceiling, audience, etc.
   • Outside: obstructions (buildings etc.), ground surface, wind, atmospheric effects...
5. A musical example
   • A solo violin produces about 1 mW of audible sound.
   • At a distance of 4 m, standing on a hard floor, this is sound is spread over an area of 100 m².
   • So the sound intensity if 1/100 mW/m² or 10^-5 W/m².
   • This translates into 70 dB, forte.
6. loudness
   • The decibel scale attempts to encompass the dynamic range of the human ear
   • It does not take into account the strong frequency dependence of our hearing
   • e.g. 120 dB at 1 kHz is intensely annoying and verging on deafening
   • 120 dB at 10 Hz we can feel but not hear
   • 120 dB at 100 kHz we can neither hear nor feel
   • Nominally we can hear sounds from 20 Hz to 20 kHz (10 kHz if you are 60+)
   • Understanding and appreciation of speech and music depends on range 125 Hz to 8 kHz
   • This is the range an audiologist tests
7. Phons
   • “Phons” are a modification of the dB scale intended to take into account our perception of loudness.
   • Phons were originally defined by Fletcher and Munson in the 30s.
   • In 2003 the International Standards Organization redefined phons to take into account the large amount of high-quality data now available.
   • The loudness in phons is defined to be equal to the SPL in dB at 1 kHz
   • At much lower and higher frequencies the loudness in phons is generally less than the SPL in dB, because here our ears are not so acute as at 1 kHz.
   • The standard is called ISO 226:2003 https://en.wikipedia.org/wiki/Equal-loudness_contour (Horizontal axis is frequency!)
   • How to read this plot:
   • At a frequency of 1 kHz at 60 dB sound has a loudness of 60 phons (by definition).
   • At a low frequency of 100 Hz, a SPL of 78 dB has a loudness of 60 phons.
   • At a high frequency of 10 kHz, a SPL of 74 dB has a loudness of 60 phons.
   • At an ultra-low frequency of 10 Hz, a SPL of 108 dB has a loudness of 60 phons.
   • At an ultra-high frequency of 15 kHz, a SPL of 70 dB has a loudness of 60 phons if you are young and healthy, but if you are over 50 you probably cannot hear it at all.
8. Music and speech
   • Adding sounds of equal frequency
   • The decibel/phon scale addresses a simple question:
   • If I can easily hear one violin:
   • Why doesn’t a pair of violins playing in unison sound twice as loud?
   • Why doesn’t the whole violin section of an orchestra deafen me?
   • Answer:
   • The decibel (and phon) scale is not simply scalable (not linear, but logarithmic)
   • Rule: double the sound, add 3 dB to the original SPL.
   • Two violins each individually playing produce an SPL of 90 dB at your ear.
   • Two such violins playing together produce 93 dB at your ear.
   • How many such violins would it take to hurt your ears (120 dB)?
   • Answer: to add 30 dB requires 10 doublings, i.e. 2¹⁰ = 1024 (hard to get this many fiddlers in the same physical location).
9. Sones
   • Just when you thought this was getting too complicated:
   • To address the problem of perceived loudness, another new measure was developed:
   • Let’s not go there; enough is enough for one lecture.
10. Noise
    • One person’s music is another person’s noise -
    • Sound-induced stress depends on a lot more than dB
    • What can make it worse:
    • Identifiable pitch (e.g. whining fans)
    • Information content (e.g. phone conversations)
    • Antipathy to the source (e.g. wind turbines)
    • “dBA” means dB frequency-weighted for human hearing.
    • Permitted noise exposure in the workplace https://www.worksafebc.com