Grade by Grade
E. Waves and Sound · Waves and Sound

Sound: A Longitudinal Pressure Wave

E3.1 E2.1 E3.6About 65 minutes
Learning goals
  • I can explain how a vibrating object produces compressions and rarefactions in air.
  • I can relate pitch to frequency and loudness to amplitude.
  • I can state the range of human hearing and define infrasonic and ultrasonic sound.
  • I can describe how the ear receives sound and turns it into nerve signals.

Words to know

sound
A longitudinal mechanical wave of pressure changes, produced by a vibrating object and carried by a medium.
compression (in sound)
A region where air molecules are crowded together: higher pressure than normal.
rarefaction (in sound)
A region where air molecules are spread out: lower pressure than normal.
pitch
How high or low a sound seems. Pitch depends mainly on frequency.
loudness
How strong a sound seems. It depends mainly on the amplitude (the size of the pressure changes).
audible range
The frequencies a listener can hear; for young people about 20 Hz to 20 000 Hz.
infrasonic
Sound with frequencies below about 20 Hz, too low for humans to hear.
ultrasonic
Sound with frequencies above about 20 000 Hz, too high for humans to hear.
timbre (sound quality)
The character of a sound that lets you tell a flute from a violin playing the same note; it comes from the mix of harmonics.

Feel the sound

Put your fingers lightly on the front of your throat and hum. You can feel the vibration. Every sound you have ever heard started with something vibrating: vocal cords, a guitar string, a speaker cone, a skate blade scraping the ice. In this lesson you will look closely at what those vibrations do to the air, and how your ears turn them back into something your brain understands.

Remember from Grade 4

In Grade 4 (Light and Sound) you learned that sound is caused by vibrations, that pitch is how high or low a sound is, that loudness is how strong it is, and that sound travels through solids, liquids and gases but not through a vacuum. Now you will describe these ideas with frequency, amplitude and pressure.

Making a sound wave

Think about one prong of a tuning fork. When it moves outward, it shoves the nearby air molecules together, making a region of slightly higher pressure: a compression. When it swings back, it leaves a region where the molecules are spread out, with slightly lower pressure: a rarefaction. The fork does this hundreds of times a second, so a train of compressions and rarefactions travels outward.

Each air molecule only jiggles back and forth a tiny distance along the direction the sound travels. That makes sound a longitudinal wave. It is easiest to graph sound as a pressure wave: pressure above normal at compressions and below normal at rarefactions. That graph looks like a transverse wave, but remember that it is a graph of pressure, not a picture of the air.

CCCRRRhighlownormalair pressureλ (compression to compression)
Top: air molecules in front of a tuning fork bunch up in compressions (C) and spread out in rarefactions (R). Bottom: a graph of air pressure along the same line. Compressions are pressure highs; rarefactions are lows. One wavelength is from one compression to the next.

Pitch and loudness

  • Pitch ↔ frequency. A higher frequency sounds higher in pitch. Doubling the frequency raises a musical note by one octave.
  • Loudness ↔ amplitude. Bigger pressure changes carry more energy and sound louder. (Loudness and the decibel scale are covered in their own lesson in this unit.)
  • Timbre ↔ waveform shape. A tuning fork makes a nearly pure sine wave. Instruments and voices add harmonics, which change the shape of the wave but not its basic frequency.

Hearing range

Young people with healthy hearing can hear about 20 Hz to 20 000 Hz (20 kHz). The upper limit drops with age and with damage from loud noise; many adults cannot hear much above 15 kHz.

  • Sound below 20 Hz is infrasonic (infrasound).
  • Sound above 20 kHz is ultrasonic (ultrasound).

Other animals hear different ranges. Elephants communicate partly with infrasound, and bats and dolphins use ultrasound to find food. You will look at these in the lesson on echolocation.

infrasonicbelow 20 Hzaudible to most humansabout 20 Hz to 20 000 Hzultrasonicabove 20 000 Hz20 Hz20 kHzelephants and largewhales use somevoices, music, most everyday sounds(upper limit drops with age)bat and dolphin calls,medical ultrasoundSound frequencies (not to scale)
The sound spectrum. Humans hear the middle band. Infrasound is too low and ultrasound is too high for us to hear, but other animals and many technologies use them.

How you hear

  1. Outer ear: the outer ear funnels sound down the ear canal to the eardrum, a thin membrane that vibrates with the pressure changes.
  2. Middle ear: three tiny bones (the hammer, anvil and stirrup, also called the malleus, incus and stapes) pass the vibrations along and concentrate their force onto a small membrane called the oval window.
  3. Inner ear: the oval window makes the fluid inside the snail-shaped cochlea move. Thousands of tiny hair cells in the cochlea bend and send electrical signals along the auditory nerve to the brain. Different parts of the cochlea respond to different frequencies.

Hair cells that are damaged by very loud sound do not grow back in humans. That is why protecting your hearing matters.

sound inaireardrumvibrates3 tinybonescochleafluidhaircellsnerve tobrainouter earmiddle earinner ear
The chain of hearing: a pressure wave in air becomes vibration of the eardrum and middle-ear bones, then waves in the fluid of the cochlea, and finally nerve signals.
Worked example

Example 1: A tuning fork

A 256 Hz tuning fork sounds in air where v = 343 m/s. (a) Find the wavelength. (b) How far is it from the centre of a compression to the centre of the next rarefaction? (c) How many compressions leave the fork each second?

  1. (a) λ = v/f = 343 ÷ 256 = 1.34 m.
  2. (b) A compression and the next rarefaction are half a wavelength apart: 1.34 ÷ 2 = 0.670 m.
  3. (c) One compression per cycle, so 256 compressions per second.

(a) 1.34 m (b) 0.670 m (c) 256

Worked example

Example 2: Comparing two sounds

Sound P has a frequency of 300 Hz and a pressure amplitude of 0.020 Pa. Sound Q has 600 Hz and 0.010 Pa. Which has the higher pitch? Which is louder? What is the musical relationship between them?

  1. Pitch follows frequency: Q (600 Hz) has the higher pitch.
  2. Loudness follows amplitude: P (0.020 Pa) has the bigger pressure changes, so P is louder (for frequencies our ears respond to about equally well).
  3. 600 Hz is double 300 Hz, so Q is one octave higher than P.

Q is higher in pitch; P is louder; Q is an octave above P.

Worked example

Example 3: Can we hear it?

Classify each sound as infrasonic, audible or ultrasonic: (a) 12 Hz rumble from a large ship's engine, (b) 3.5 kHz smoke-alarm beep, (c) 40 kHz bat call, (d) 2.5 MHz medical ultrasound.

  1. Compare each with 20 Hz and 20 000 Hz.
  2. (a) 12 Hz < 20 Hz: infrasonic. (b) 3500 Hz is between the limits: audible. (c) 40 000 Hz > 20 000 Hz: ultrasonic. (d) 2 500 000 Hz: ultrasonic.

(a) infrasonic (b) audible (c) ultrasonic (d) ultrasonic

Just for fun

Funny-but-true: a smoke-alarm beep is pitched right in the range where human ears are most sensitive (a few thousand hertz). That is no accident. It is designed to be hard to miss. (Surprisingly, studies show many children can sleep through one, which is a good reason for every family to have a fire-escape plan.)

Hands-on activity

Make sound visible

You need: a large bowl, plastic food wrap, an elastic band, a pinch of dry rice (or salt), a metal pot and a wooden spoon. Bang the pot gently to moderately, never close to anyone's ears.

  1. Stretch the plastic wrap tightly over the bowl like a drum and hold it in place with the elastic band.
  2. Sprinkle a few grains of rice on the wrap.
  3. Hold the pot about 20 cm from the bowl and bang it with the spoon. Watch the rice.
  4. Try banging softly and then harder. Try holding the pot farther away.
  5. Hum loudly with your mouth close to the wrap (without touching it).
  6. Finally, put your fingertips on your throat and say "sss" then "zzz". Which one makes your vocal cords vibrate?

What to look for: the rice jumps because the pressure waves from the pot make the plastic vibrate. Harder bangs (bigger amplitude) make the rice jump higher; moving farther away makes it jump less. You feel vibration for "zzz" but hardly any for "sss", because "z" uses your vocal cords and "s" does not.

Your turn

1

Explain how a vibrating speaker cone makes a compression and a rarefaction.

2

Is sound a transverse or longitudinal wave? Explain.

3

What property of a sound wave determines pitch? Loudness?

4

Give the approximate range of human hearing.

5

A sound has a frequency of 25 kHz. Can a person hear it? What is it called?

6

Find the wavelength in air (343 m/s) of a 20 Hz sound and of a 20 kHz sound.

7

List the parts of the ear in order, from the air to the brain.

More practice: warm-up

1

What is a rarefaction?

2

What is below 20 Hz called?

3

Which part of the ear contains hair cells?

4

A note is raised one octave. What happens to its frequency?

5

Why can't you hear a bell ringing inside a jar with all the air pumped out?

More practice: on your own

1

A sound wave in air has compressions 0.50 m apart. The speed of sound is 340 m/s. Find the frequency.

2

A student says, "Sound travels as air flowing from the speaker to my ear." Correct the statement.

3

Two notes are 220 Hz and 880 Hz. How many octaves apart are they?

4

Why do many older adults have trouble hearing high-pitched sounds?

5

A flute and a clarinet both play a 440 Hz note equally loudly. Why do they sound different?

Challenge

1

A speaker produces a pure 1.0 kHz tone. On a pressure-versus-time graph for one point in front of the speaker, how much time passes between a pressure maximum and the next minimum? If the speaker is switched to 2.0 kHz with half the pressure amplitude, describe two ways the graph changes.

2

Explain why the middle-ear bones are needed. (Hint: air is easy to move; the fluid in the cochlea is much harder to move.)

3

A thunderstorm produces sounds from about 5 Hz to several thousand hertz. Which parts of the thunder can you hear? Why might the rumble seem to "shake" a house even though you cannot hear all of it?

Check your understanding

Quiz

1.

A compression in a sound wave is a region of…

2.

The pitch of a sound depends mainly on its…

3.

Which sound is ultrasonic?

4.

In the ear, sound vibrations are changed into nerve signals by…

5.

Doubling the frequency of a note raises it by…

6.

Sound is described as longitudinal because…

For parents and teachers

Big idea: students explain how sound is produced, transmitted and received (E3), using correct vocabulary (E2.1), and connect sound to the longitudinal-wave model (E3.1). The hearing range sets up E3.6 (infrasonic and ultrasonic hearing) later in the unit.

How to help: Do the rice-drum activity. Free online tone generators are a fun way to test your own hearing range (keep the volume low!); teens often hear tones that parents cannot.

Common difficulties:

  • Treating the pressure graph as a picture of the air. It is a graph.
  • Thinking air flows from the source to the ear.
  • Confusing pitch (frequency) with loudness (amplitude).