Describe sound as a longitudinal wave that needs a medium, relate its frequency to pitch and its amplitude to loudness, and describe how its speed depends on the medium (MA STE Introductory Physics, Waves, HS-PS4-1).

What this topic is asking

Sound is the everyday wave the Massachusetts Introductory Physics MCAS uses to test wave ideas. You must describe sound as a longitudinal wave that needs a medium, relate its frequency to pitch and its amplitude to loudness, and describe how its speed depends on the medium. The crosscutting ideas are cause and effect (what you change about the wave changes what you hear) and structure and function (the medium's structure sets the speed). This builds directly on the transverse-versus-longitudinal distinction.

Sound needs a medium

The MCAS expects you to know that sound is mechanical: it must have a medium to travel through. A ringing bell inside a jar from which the air is pumped out goes silent, even though you can still see it vibrating, because there is no air to carry the sound. This is the key difference from light, which is an electromagnetic wave and travels through empty space. Sound spreads through air, water, and solids, but not through the vacuum of space.

Pitch and loudness

This is a frequent MCAS test point, and the trap is mixing the two up:

• Pitch comes from frequency. A piccolo plays high-frequency, high-pitched notes; a tuba plays low-frequency, low-pitched ones. The human hearing range is roughly $20$ Hz to $20{,}000$ Hz.
• Loudness comes from amplitude. Plucking a guitar string harder gives it a bigger amplitude and a louder sound, without changing the pitch. Turning up the volume increases amplitude, not frequency.

Keeping pitch tied to frequency and loudness tied to amplitude is exactly what the standard asks for.

The speed of sound depends on the medium

Because the speed depends on the medium, the same sound can speed up or slow down as it passes from one material to another. In air, sound travels at roughly $340$ m/s; in water it is several times faster; in steel, faster still. The wave equation $v = f\lambda$ holds in each medium, so when sound enters a faster medium at the same frequency, its wavelength gets longer. The medium dependence also explains why you hear an approaching train through the rails before you hear it through the air.

Worked example

Reference-sheet note

The reference sheet gives the wave equation $v = f\lambda$, which you use to find a sound's wavelength from its frequency and speed. What you recall is that sound is longitudinal and needs a medium, that frequency sets pitch and amplitude sets loudness, and that sound travels fastest in solids and slowest in gases because of how the particles are spaced and bound.

Try this

Q1. State what property of a sound wave determines its pitch, and what determines its loudness. [2]

• Cue. Frequency determines pitch (higher frequency, higher pitch); amplitude determines loudness (larger amplitude, louder).

Q2. A $680$ Hz sound travels through air at $340$ m/s. Calculate its wavelength. [2]

• Cue. $\lambda = \dfrac{v}{f} = \dfrac{340}{680} = 0.50$ m.