The Fundamentals of Sound

Will Styler - LIGN 113

Now we’re pivoting into sound

• We’re going to focus on the elements of sound that are crucial for understanding hearing.

• … and we’ll skip some of the other fun stuff!

Today’s Plan

• What are the properties of sound?

• How can we visualize them?

Sound is compression and rarefaction in a medium

… but we need to talk about it more concretely!

The Key Properties of Sound

• Duration

  • How long does it last?

• Amplitude

  • How powerful is it?

• Frequency

  • How often does it cycle?

• Period

  • How long does a single cycle take?

Key Properties Continued

• Wavelength

  • How far can the wave travel in a single cycle?

  • What is the physical distance between peaks?

• Phase

  • That’s next time!

Duration

• We talk about sounds in Milliseconds

  • 1 second (s) = 1000 milliseconds (ms)

  • Half a second (0.5 s) = 500 milliseconds (ms)

  • One Quarter second (0.25 s) = 250 ms

  • 1 meter = 1000 millimeters

• Duration is kind of boring for this class

  • … but very important for language and survival

Amplitude

• What is the difference in pressure between compressions and rarefactions?

• We talk about Amplitude in Decibels

• We’ll get there soon!

Amplitude is related to loudness

• Loudness is the perceptual correlate of amplitude

• Generally, when amplitude goes up, so does perceived loudness

• It’s super complicated!

  • More on this later

Conceptualizing Amplitude

• Why is dropping a small book quieter than dropping a large one?

• Why can high amplitude sound be damaging and shatter windows?

• How does a car muffler work?

Period

• How long does a single cycle last?

• Here, 0.005 seconds (5 ms)

• Here, 0.0025 seconds (2.5ms)

Frequency

• “How many times does the sound cycle in one second?”

• Measured in ‘Hertz’ (Hz), also known as ‘Cycles per second’

• ‘How many periods can fit in one second?’

f = 1/t

• f = Frequency in Hz
• t = Period in Seconds

• Period = 0.005 seconds
• Frequency = 1/0.005 = 200 Hz

• Period = 0.0025 seconds
• Frequency = 1/0.0025 = 400 Hz

• Period = 0.0025 seconds
• Frequency = 1/0.0025 = 400 Hz

Greater period = Lower Frequency!

• Longer cycles == Fewer Cycles per Second

Frequency is related to pitch

• Pitch is the perceptual correlate of frequency

• Generally, when frequency goes up, so does perceived pitch

• It’s complicated!

  • More on this later!

Wavelength

• “How far does the wave travel during a single cycle?”

Calculating Wavelength requires two pieces of information…

• How fast is it moving?

  • At the speed of sound! (343 meters per second)

• How often per second does it cycle?

  • That’s the frequency!

It makes sense that frequency is involved

Wavelength is…

• Meters per second / Cycles per second

• You then get meters per cycle!

λ = c/f

• λ = Wavelength in Meters

• c = Speed of Sound in Air (343 m/s for this class)

• f = Frequency in Hz

• Period = 0.005 seconds
• Frequency = 1/0.005 = 200 Hz
• Wavelength = 343/200 = 1.715 Meters

• Period = 0.0025 seconds
• Frequency = 1/0.0025 = 400 Hz
• Wavelength = 343/400 = 0.857 Meters

Lower Frequencies have longer wavelengths

Conceptualizing Wavelength

• Why does a double-bass play lower notes than a violin?

• Why do subwoofers need to be bigger?

• Why do you hear your neighbors’ bass, but not their treble?

  • There are also differences in reflection of low vs. high frequencies

Period, Frequency, and Wavelength are all related

• Frequency is calculated from period, wavelength from frequency

Amplitude and Duration are not related to any other element!

• Nor to each other!

We can find these things out for any sound!

• Amplitude ≈ 0.4
• Duration = ??
• Period = 0.01 seconds
• Frequency = 1/0.01 = 100 Hz
• Wavelength = 343/100 = 3.43 meters

Wrapping Up

• All sounds have amplitude, duration, periods, frequencies, and wavelengths

• Many of these things are related to one another

• These properties have real consequences for how sound actually works!

For Next Time

• What was up with that last sound?

• And why was it so bumpy?

Thank you!