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Longitudinal oscillations produce regions of compressions and rarefactions.

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The vibrating forks produces compressions and rarefactions, which propagate away from the source.

We can apply the concept of phase to any repetitive periodic motion. One complete cycle corresponds to 360° or 2π rad. Half-a-cycle corresponds to 180° or π rad. A quarter-cycle coreesponds to 90° or π/2 rad. So on and forth.

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These four oscillations are in-phase with one another (phase difference of 0, 2π, 4 π, …)

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The 1st and the 3rd are complete out-of-phase (phase difference of π, 3π, 5 π, …) with the 2nd and the 4th.

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Each oscillation lags the one on the left a quarter-cycle (π/2 rad).

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Each oscillation lags the one on the left by 1/8 of a cycle (45° or π/4 rad).

The profiles of two progressive waves moving from left to right are now clearly visible. There is the transverse wave in the bobbing heads, and the longitudinal wave in the gyrating hips. 😛

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In an actual progressive wave, there is a continuous increasing phase lag in the direction of wave propagation. Each wave element lags the preceding wave element by a bit.

Notice that a wave crest always advances by one wavelength after every one period? That’s why v=λ/T, or v=fλ.

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v=fλ

For the same medium, wave speed is constant. So when frequency goes up, wavelength does down. In the animation below, both waves have the same speed. So doubling the frequency always result in halving of wavelength.

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v=fλ

In different medium, the wave speed is different. When a wave crosses from one medium to another, the frequency does not change, but the speed and wavelength do. In the animation below, both waves have the same frequency. The one with the longer wavelength propagates at a faster speed.

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For the original 🍏, click <here>

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Transverse Wave

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Longitudinal Wave

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Water wave is an example of a 2D wave that propagates along a surface.

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Notice the bob does not travel with the wave. The motion of the wave particles are different from the “motion” of the wave.

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Each medium particle oscillate about its own equilibrium position. Their oscillatory motion result in the propagation of the energy/momentum.