Wave speed

Essential knowledge 14.1.A.3: the speed at which a wave or wave pulse propagates through a medium depends on the type of wave and the properties of the medium. Notice what is missing from that list. The source is not in it.

That is the sentence that costs marks. Turn the dial on a signal generator and the frequency of the sound rises. The speed does not. Since the sheet prints

something has to absorb the change, and it is the wavelength: raise $f$ and $\lambda$ shrinks in exact proportion, leaving $v$ where it was. EK 14.2.A.3 states the same dependence, that wavelength is proportional to the wave's speed and inversely proportional to its frequency.

The rule flips at a boundary, and for the same reason. EK 14.3.A.1.iv: the frequency of a wave does not change when it travels from one medium to another. Now the medium is what changed, so $v$ changes, and $\lambda$ moves with it while $f$ holds still. One medium, fixed $v$: frequency is free. New medium: frequency is the fixed one.

What sets $v$ in the AP cases. Tension and mass per length for a string, through $v_{\text{string}} = \sqrt{F_T/(m/\ell)}$ (14.1.A.3.ii). Temperature for sound in a given medium (14.1.A.3.iii). And nothing at all in vacuum, where $c = 3.00 \times 10^8$ m/s is a universal constant (14.1.A.3.i).

The rearrangements and the graph reading live in the wave speed guide.