Two waveforms: one has crowded, short crests; the other has widely spaced, tall crests. How do the sounds differ?

Crest spacing is frequency, which is pitch. Crest height is amplitude, which is loudness. The first is high and quiet; the second is low and loud

You turn up the volume knob on a radio. What changes in the wave?

The pitches of the notes in the tune do not change. Only the loudness changes. The amplitude grows; the frequency stays exactly as it was

The tuning A is 440 hertz. What is the frequency of the A one octave above?

Going up an octave doubles the frequency. 440 times 2. 880 hertz

Waves and Sound · Grade 9

Is a high-pitched sound necessarily a loud one?

No — these are two entirely separate quantities. Pitch is set by frequency: more cycles per second means a higher note. Loudness is set by amplitude: a bigger vibration means a louder sound. A child's whisper can be high and faint at once, and thunder can be low and deafening.

Learning objectives

Match a described change in a sound to a change in either its frequency or its amplitude
Read two waveforms side by side and say which sound is the higher and which is the louder
State the range of frequencies a human ear can hear and place ultrasound and infrasound outside it
Explain what the decibel scale measures and from what level noise begins to damage hearing

Frequency sets pitch

Pitch is what separates a low note from a high one, and it is set purely by frequency. More cycles per second means a higher note.

On a diagram a high note looks like a crowded wave, with crests close together. A low note looks stretched out, with crests far apart. None of this has anything to do with how tall the crests are.

The orchestral tuning A is 440 hertz. The A one octave above it is exactly 880 hertz — double. That is the rule: each octave upwards doubles the frequency.

Amplitude sets loudness

Loudness is set by amplitude, that is by how large the vibration is. A bigger vibration squeezes the air harder and carries more energy.

On a diagram a loud sound is a tall wave and a quiet one is a short wave, with no change at all in how closely the crests are spaced. The volume knob on a speaker changes amplitude and never touches frequency.

So two waveforms side by side are read with two separate questions. How closely packed are the crests — that is the pitch. How tall are they — that is the loudness. A change in one does not require a change in the other.

What the ear hears, and when it is damaged

The human ear picks up roughly 20 to 20,000 hertz. Below that range lies infrasound — earthquakes and elephants; above it lies ultrasound, used in pregnancy scans and sonar, and used by bats.

The range narrows with age, mostly at the top end. A forty-year-old typically hears up to about 15,000 hertz, and that is normal rather than an injury.

Loudness is measured in decibels on a logarithmic scale: every ten decibels is a factor of ten in energy. Ordinary conversation is about 60 decibels, busy traffic about 80, a concert about 110. Sustained exposure above 85 decibels causes permanent hearing damage, and that damage is never repaired.

Worked examples

Two waveforms: one has crowded, short crests; the other has widely spaced, tall crests. How do the sounds differ?
1. Crest spacing is frequency, which is pitch
2. Crest height is amplitude, which is loudness
Answer: The first is high and quiet; the second is low and loud
You turn up the volume knob on a radio. What changes in the wave?
1. The pitches of the notes in the tune do not change
2. Only the loudness changes
Answer: The amplitude grows; the frequency stays exactly as it was
The tuning A is 440 hertz. What is the frequency of the A one octave above?
1. Going up an octave doubles the frequency
2. 440 times 2
Answer: 880 hertz

Common mistakes

Treating a high note as a loud note: "High" describes frequency and "loud" describes amplitude. A sharp whisper is high and quiet at the same time, and deep thunder is low and loud — the two quantities are independent.
Reading the decibel scale as an ordinary scale: It is logarithmic. 80 decibels is not twice 40 but ten thousand times the energy, so a small difference in the number is an enormous difference in practice.
Treating hearing damage as something that wears off: The hair cells in the inner ear do not grow back. Sustained exposure above 85 decibels destroys them permanently, and the loss accumulates over years with no pain to warn you.

What to remember

Frequency = pitch. Amplitude = loudness.
On a diagram: spacing versus height.
The ear hears about 20 to 20,000 hertz.
Above 85 decibels the damage is permanent.