Sound Waves – Loudness, Amplitude, Oscilloscopes, Pitch & Frequency

Types of Waves

• Transverse: the stuff that makes up the wave wiggles up and down or side to side, but the wave itself moves forward.

• Longitudinal: the stuff wiggles back and forth, in the same direction the wave is moving; think of sound waves.

Wave Properties (for all waves)

• Amplitude: how tall the wave is, from the middle line to its highest point (crest) or lowest point (trough).

• Wavelength $\lambda$: the distance between two identical spots on neighboring waves (like from one peak to the next).

• Frequency $f$: how many full waves pass by in one second; the unit is Hertz (Hz), so $1\,\text{Hz}$ means 1 wave per second.

  • If a wave's speed stays the same, then if you have lots of waves per second ($f$), they must be squished closer together ($\lambda$ is smaller).

Amplitude & Loudness

• Bigger waves (larger amplitude) mean louder sounds; smaller waves (smaller amplitude) mean softer sounds.

• Changing how loud a sound is involves changing its energy. An amplifier just makes the electrical signal bigger before it goes to the speaker, making the sound louder.

Frequency & Pitch

• More waves per second (higher $f$) means a higher-pitched sound; fewer waves per second (lower $f$) mean a lower-pitched sound.

• The pitch of a sound depends ONLY on its frequency, not how big the wave is (amplitude).

Oscilloscopes (drawing waves)

• A microphone changes sound (which is a back-and-forth wiggle) into an electrical wiggle that an oscilloscope can draw as an up-and-down wave.

• The height of the drawn wave shows how loud it is (amplitude); how spread out the waves are shows how long each wave takes ($T$), which helps us figure out how many waves there are per second ($f = 1/T$).

• When comparing drawn waves:

  • If two sounds have the same pitch but different loudness, their drawn waves will be spaced the same but have different heights.

  • A higher-pitched sound will have its drawn waves squished closer together (more waves per second).

What Humans and Animals Can Hear

• Humans (when young): can hear sounds from $\mathbf{20\,\text{Hz}}$ (a really deep rumble) up to $\mathbf{20,000\,\text{Hz}}$ (a super high squeak).

  • The ability to hear super high sounds gets worse as you get older.

• Animals (some examples):

  • Elephant: $\mathbf{16\text{–}12,000\,\text{Hz}}$ (they can hear some sounds too low for us).

  • Dog: $\mathbf{67\text{–}45,000\,\text{Hz}}$.

  • Bat: $\mathbf{2,000\text{–}110,000\,\text{Hz}}$ (they use super high sounds too high for us to navigate).

Musical Instruments & Timbre

• The same musical note (meaning the same main frequency) sounds different on different instruments like a guitar versus a piano. That's because instruments also make other, quieter sounds called 'harmonics' (which are just multiples of the main frequency).

• Timbre: This is the unique quality or character of a sound, completely determined by which harmonics are present and how strong they are.

Simple Rules & Meanings

• Loudness goes with how big the wave is (Amplitude).

• Pitch goes with how many waves per second (Frequency).

• Amplitude: how high or low the wave goes from its middle line.

• Wavelength $\lambda$ and frequency $f$ are tied to how fast the wave moves ($v$) with this simple rule: $v = f\lambda$