A larger amplitude makes a sound louder

1. The amplitude of a sound wave is the maximum distance the particles of the air are pushed from their undisturbed positions as the wave passes.
2. A larger amplitude gives a louder sound, and a smaller amplitude gives a quieter sound.
   1. A source with a larger amplitude vibrates further on every swing, so it drives the air in front of it harder.
   2. Its compressions are squeezed more tightly and its rarefactions are stretched more thinly, so the wave carries more energy each second.
   3. Your eardrum is then pushed and pulled through a greater distance as each wave arrives, and you register that as a louder sound.
3. Turning up the volume on a loudspeaker makes its cone travel further backwards and forwards, while the number of times it moves each second stays the same.
4. Clapping harder gives a louder clap because your hands set the air moving through a greater distance, not because the clap happens any more often.

A higher frequency is heard as a higher pitch

1. The frequency of a sound wave is the number of complete waves that pass a point each second, measured in hertz, $Hz$.
2. A higher frequency gives a higher pitch, and a lower frequency gives a lower pitch.
   1. A source vibrating at a higher frequency sends out more compressions every second, so more of them arrive at your ear in each second.
   2. Your ear reports that faster stream of arrivals as a higher note.
3. The A string of a violin tuned to $440Hz$ sends $440$ compressions into your ear each second, and the note one octave above it, at $880Hz$, sends twice as many.
4. A human ear responds to frequencies from about $20Hz$ to $20000Hz$, and a vibration outside that range gives no sensation of sound however strong it is.
   1. The upper limit falls with age, so an adult may hear nothing above about $12000Hz$ while a child in the same room hears it easily.
5. Pitch and frequency are two views of one thing: frequency is the measured number of waves per second, pitch is how your ear reports that number.

Amplitude and frequency can be changed one at a time

1. Changing the amplitude changes the loudness and leaves the pitch exactly where it was.
2. Changing the frequency changes the pitch and leaves the loudness exactly where it was.
3. Two sounds with the same frequency but different amplitudes are the same note, one louder than the other, like a piano key struck gently and then struck hard.
4. Two sounds with the same amplitude but different frequencies are equally loud but different notes, like two guitar strings plucked with the same force.
5. Frequency also has no effect on how fast the sound travels, so a high note and a low note leaving an instrument together reach you together.

An oscilloscope shows amplitude as height and frequency as spacing

1. A microphone turns the pressure variations of a sound wave into a varying p.d., and an oscilloscope draws that p.d. against time as a trace on its screen.
2. The height of the trace above the centre line shows the amplitude, so a taller wave means a louder sound.
3. The number of complete waves across the screen shows the frequency, so more waves in the same screen width means a higher pitch.
   1. Each wave takes up less width when the frequency is higher, because one complete vibration then takes less time.
4. A comparison of two traces only means anything if the settings are identical for both of them.
   1. The time base, which sets how much time one horizontal division stands for, must be left untouched, or a low note can be made to look like a high one.
   2. The gain, the vertical sensitivity that sets how many volts one vertical division stands for, must also be left untouched, or a quiet sound can be made to look loud.
   3. The microphone should stay the same distance from the source, because a sound that has spread further arrives with a smaller amplitude.

Instruments set their pitch by how fast the source vibrates

1. Pressing a guitar string against a fret shortens the vibrating length, so the string vibrates more times each second and the pitch rises.
2. Tightening the string with its tuning peg also raises the pitch, because a tighter string springs back faster and so vibrates at a higher frequency.
3. Slackening the string, or letting a longer length of it vibrate, lowers the frequency and drops the pitch.
4. Plucking that same string harder moves no fret and changes no tension, so the note stays put and only the loudness rises.
5. A bass drum has a wide, slack skin that vibrates slowly, giving frequencies of only a few tens of hertz, near the bottom of the audible range.
6. A cymbal is a thin metal disc that vibrates rapidly, giving frequencies of several thousand hertz, near the top of the range.
7. Either one can be played softly or deafeningly, which shows that where an instrument sits in the frequency range says nothing about how loud it can be.