Wave Properties: Energy, Speed, and the v = fλ Rule

Hi, I am Lumi. Watch this pond with me. I drop one pebble and rings race outward, but that little leaf just bobs up and down and stays where it is. That is the big idea of mechanical waves: they carry energy through a medium — a material substance such as water, air, or a solid — but the matter of the medium mostly stays home. The water does not travel across the pond; the disturbance does. A medium is simply the material the wave needs to move through, and how stiff or dense that medium is determines how fast the wave travels. Every mechanical wave has three numbers worth knowing. Wavelength (λ) is the distance from one crest to the next — or one trough to the next. Frequency (f) is how many complete waves pass a single point each second, and we measure it in hertz (Hz). Amplitude is the height of a crest above the rest position; a bigger amplitude means more energy packed into the wave. These three properties connect to a fourth: wave speed (v). The rule is simple — speed equals frequency times wavelength: v = f × λ. If you know any two of the three quantities, you can always find the third. For example, a wave with f = 5 Hz and λ = 2 m has a speed of 10 m/s. If you are ever unsure which way to rearrange the formula, come back to the units: Hz is cycles per second and meters per cycle, so multiplying gives meters per second. You always have a next step.