Sound Waves Notes

Sound Waves

How sound travels and how we hear it.

Properties of Sound

  • Sound waves are longitudinal waves.
  • When a tuning fork vibrates, it creates areas of high pressure (compressions) and low pressure (rarefactions).
  • As the tines of the fork vibrate back and forth, they push on neighboring air particles to the right.
  • The backward retraction of the tine creates a low-pressure area allowing the air particles to move back to the left.

Speed of Sound

  • Sound needs a medium to travel: solid, liquid, gas.
  • The speed of sound in air depends on its temperature: v_{sound} = 331 + 0.6T
  • Generally, we use 343 m/s (sea level, room temperature: 20°C).
  • Sound travels faster in solids and liquids than in gases.

Speed of Sound Examples

  • Air (0°C): 331 m/s
  • Air (20°C): 343 m/s
  • Water (25°C): 1493 m/s
  • Sea Water: 1533 m/s
  • Copper: 3560 m/s
  • Iron: 5130 m/s
  • Glass: 5640 m/s
  • Diamond: 12,000 m/s

Sound Loudness

  • Related to the amplitude of the sound wave
  • Amplitude is the measure of the variation in pressure along the wave.
  • Small pressure variations are perceived as softer sounds than those with large pressure variations.
  • The larger the pressure variation, the more it "hurts" to listen to the sound.
  • Loudness is perceived differently by different people.

Sound Intensity

  • Intensity is the power of the sound per unit area, also known as sound level, and depends on the energy of the wave.
  • Measured in decibels (dB).
  • Measured by comparing the pressure variation of a sound to the pressure variation of the softest audible sound (0 dB).
  • A 10 dB increase in sound is typically perceived as "twice as loud."

Decibel Scale

  • Decibels (dB) are measured by comparing the pressure variation of a sound.
  • Changes in Air Pressure:
    • 2 times: +6 decibels
    • 10 times: +20 decibels
    • 100 times: +40 decibels
    • 1,000 times: +60 decibels
    • 10,000 times: +80 decibels
    • 100,000 times: +100 decibels
    • 1,000,000 times: +120 decibels
    • 10,000,000 times: +140 decibels

The Decibel Scale: Sound Levels

  • 120 dB: Jet airplane taking off (Painful)
  • 90 dB: Heavy truck (Very noisy)
  • 70 dB: Inside compact car (Noisy)
  • 50 dB: Average classroom (Moderate)
  • 30 dB: Bedroom at night (Quiet)
  • 10 dB: Soft whisper (Barely Audible)
  • I_0 = 1 \times 10^{-12}

Ranking Sounds on the Decibel Scale (Lowest to Highest)

  • Threshold of Hearing (0 dB)
  • Rustling Leaves (30 dB)
  • Light Rainfall (40 dB)
  • Running Dishwasher (55 dB)
  • Vacuum Cleaner (60 dB)
  • Alarm Clock (75 dB)
  • Jack Hammer (100 dB)
  • Fire Alarm at School (105 dB)
  • iPod at Max Volume (120 dB)
  • Threshold of Pain (120 dB)
  • Excited Crowd (127 dB)
  • Rifle Shot (~140 dB)
  • Rock Concert (~150 dB)

Pitch

  • The pitch of a sound is associated with its frequency.
  • When particles vibrate more quickly, a higher sound is produced.
  • Higher frequency means higher pitch.

Range of Hearing

  • The maximum range for human hearing is between 20 Hz and 20 kHz (20,000 Hz).
  • Most sensitive to 400 Hz to 7,000 Hz.
  • Elephants can hear 16 Hz – 12 kHz.
  • Dogs can hear 50 Hz – 35 kHz.
  • Cats can hear 45 Hz – 85kHz.
  • Bats can hear over 100 kHz!

How We Hear

  1. Sound enters your ear!
  2. Sound vibrates your eardrum.
  3. The bones in your ear vibrate.
  4. The fluid in the cochlea moves.
  5. Nerves carry the energy to your brain, these nerves correspond to frequency! The brain interprets these signals as sound!

How We Make Sound

  • Air from the lungs flows through the windpipe and into the voice box (where the vocal cords are).
  • Then the air pushes the vocal cords apart making them vibrate.
  • The vibrations create a series of sound waves that exit through your mouth.
  • The change of shape of the vocal cords changes the sound and its pitch.
  • If you can’t talk because of a cold or laryngitis, it is because your vocal cords are swollen and inflamed.

Out of Range Frequencies

  • Infrasonic frequencies are those that are LOWER than 20 Hz – “felt” vs. heard
    • Examples: some sub-woofers, thunderstorms, earthquakes, elephants
  • Ultrasonic frequencies are HIGHER than 20 kHz
    • Examples: sonar, medical ultrasounds, bats, whales, and dolphins
  • Echolocation – process in which echoes are used to determine the distance between objects
    • Used to determine size/shape of buried objects or to observe a fetus in the womb

Doppler Effect

  • The Doppler Effect is the APPARENT change in the frequency as a result of relative movement between the source of sound and the observer
    • Examples: sirens, trains, planes, etc.
  • Since velocity is constant, the apparent change in wavelength causes an apparent change in frequency.
  • When the source is moving TOWARDS you, the pitch you hear will be HIGHER than the source.
  • When it is moving AWAY from you the pitch is lower.

Doppler Effect Equation

  • Source approaching:
    f'' = \frac{v}{v - vs} f{source}
  • Receding source:
    f'' = \frac{v}{v + vs} f{source}
  • Where:
    • f'' is the observed frequency.
    • v is the velocity of sound.
    • v_s is the velocity of the source.
    • f_{source} is the source frequency.
  • \lambda ' = (v - v_s)T

Sonic Boom

  • If the source is moving at the speed of sound (or faster!), the sound waves “pile up” into a shock wave called a sonic boom.
  • Supersonic is faster than sound.
  • Subsonic is slower than sound.
  • Sonic booms sound much like pressure waves from explosions!

Mach Travel

  • Mach speeds are speeds at or above the speed of sound.
  • Mach 1 = speed of sound
  • Mach 2 = twice the speed of sound
  • To find the Mach number, find the ratio of an objects velocity to the speed of sound (how many times faster than the speed of sound): M = \frac{v}{v_{sound}}