# Why do water ripples widen (in plain English)

In this YouTube video water ripples start out with a wavelength of, say, 10 cm at the outer edge and they end up with a wavelength of about 30-40 cm towards the end of the video. Why does this happen, in simple, plain English? I can see here wave equations that produce the same result in simulations, but the equations don't give me a "feel" for why this happens. Intuitively, I'd expect the opposite: when water ripples spread out, I'd think they encounter "resistance" from the medium, so if anything, I'd expect the wavelengths at the front to decrease or "bunch up".

Several things happen with ripples.

First - they are comprised of different wavelengths. That may be hard to explain in plain English, but basically the only way that a wave can have a single wavelength is when it goes on for all infinity. A short "wave packet" must contain different wavelengths.

Next - the speed of propagation of these different wavelengths is not constant: this means that the "packet" of waves will spread out over time. Imagine the start of a running race. Initially all the runners start together, but since some are running faster than others, after a while the "field" spreads out.

As a further complication, different wavelengths will be attenuated by different amounts - the high frequency ripples are attenuated more strongly over the same distance. This means that the ripples will look "longer" as they travel further - the shorter components have been damped.

• I see, thanks. So the "wave packet", by analogy to sound, is bit like a packet of white noise: a mix of basses, midtones and trebles, all of which move at different speeds. The "basses" damp the least, so, after a while, they end up at the forefront. Commented Jun 13, 2015 at 1:57
• @MrSparkly - that's pretty good. In fact, for a wave packet to have a finite "envelope" the frequencies need to be somewhat bunched - you can't have all frequencies (that would give rise to something called a delta function - an infinitely narrow and tall spike). Commented Jun 13, 2015 at 1:59

As stated in previous answer,many things happen in water ripples.But a major reason for increment in wavelength is loss of energy as the wave progresses due to non ideal conditions.Since wavelength is inversely proportional to energy of wave,as energy decreases,wavelength increases.Hope this helps :-)

• I'm pretty sure this is incorrect. The wave will spread regardless of energy loss due to dispersivity of the medium. Even if there is no attenuation, the packet can get wider due to dispersion. Part of the problem is that you are confusing wavelength with the width of the wavepacket. As the packet spreads, nothing happens to the wavelengths of the components of the wave.
– Ian
Commented Jun 13, 2015 at 14:31