Mechanical waves & sound
The idea
A wave carries energy from place to place without carrying the medium along with it — the water bobs in place while the ripple travels. Mechanical waves need a medium and come in two geometries: transverse waves, where the medium vibrates perpendicular to the travel direction (a shaken rope), and longitudinal waves, where it vibrates along the travel direction (sound's compressions and rarefactions in air). The core relation ties the picture together: wave speed = frequency × wavelength, or v = fλ.
The crucial division of labor: the SOURCE sets the frequency, and the MEDIUM sets the speed. Wavelength is the negotiated result, λ = v/f. Sound travels at about 343 m/s in room-temperature air, faster in water, faster still in steel — stiffer media snap back quicker. Pitch corresponds to frequency and loudness to amplitude; waves also reflect from boundaries, and overlapping waves add point by point (superposition), which is how standing waves form on instrument strings.
The common misconception is that turning up the frequency makes a wave travel faster. In a fixed medium it does not: a high note and a low note from the same speaker reach you together. Raising f simply shortens λ so that their product stays pinned at the medium's speed.
Worked example
A tuning fork vibrates at 440 Hz. Find the wavelength of its sound in air, where sound travels at 343 m/s, and in fresh water, where it travels at 1480 m/s.
- Sort out what each part of the system controls: the fork fixes the frequency at 440 Hz everywhere, while each medium fixes its own wave speed.
- Rearrange v = fλ for wavelength: λ = v/f.
- In air: λ = 343/440 ≈ 0.78 m — about the height of a kitchen counter, which is why a single tone fills a room with peaks and quiet spots spaced on a human scale.
- In water: λ = 1480/440 ≈ 3.36 m. Same tone, but the faster medium stretches each cycle over more than four times the distance.
- Sanity-check the ratio: 3.36/0.78 ≈ 4.3, exactly the ratio of the two speeds (1480/343 ≈ 4.3), as it must be when frequency is held fixed by the source.
Answer. The 440 Hz sound has a wavelength of about 0.78 m in air and about 3.36 m in water — the frequency stays put while the medium stretches the wavelength.
Check your understanding
- Why does the frequency of a wave stay the same when it crosses from one medium into another, while wavelength and speed both change?
- How would you explain to a friend that the medium itself does not travel with a wave, using a stadium crowd or a rope as the picture?
- What properties of a medium make sound travel faster through it, and why is sound quicker in steel than in air?
- How does superposition of a wave with its own reflection produce a standing wave on a guitar string?
Build the foundations first
Mechanical waves & sound builds on these concepts. If any feel shaky, start there.