Lighthill's eighth power law
Imagine you are in a swimming pool, and there is a wave coming towards you. As the wave gets closer, it gets bigger and bigger until it crashes over your head. The wave's height is proportional to the energy it carries, meaning the more energetic waves are higher than less energetic ones.
Now, let's take a moment to imagine that we are standing outside, and we hear a sound. We can tell how loud it is by measuring its intensity or the strength of the sound waves reaching our ears. This intensity or energy is also directly proportional to the sound's perceived loudness, meaning louder sounds have a greater energy than softer ones.
But what happens when we have a group of swimmers or a group of sounds coming towards us? Based on our previous experiences with waves and sound, we might think that the collective energy of the group is just the sum of each individual's energy. However, that's not the case.
Here's where Lighthill's Eighth Power Law comes in. According to this law, the collective energy of a group of swimmers or sounds is actually proportional to the eighth power of their number. That might sound complicated, but let's break it down.
Imagine you have two swimmers. According to Lighthill's Eighth Power Law, the collective energy they create by their movements is proportional to 2^8, or 256. If you have three swimmers, the collective energy increases to 3^8, or 6,561. And if you have ten swimmers, the energy increases to 10^8, or 100,000,000.
Similarly, if you have two sounds, the collective energy they create is proportional to 2^8 or 256. If you have three sounds, the collective energy increases to 3^8 or 6,561. And if you have ten sounds, the energy increases to 10^8 or 100,000,000.
This exponential increase in energy means that we can't just add up the energy of each individual to get the total collective energy. It also suggests that larger groups can create much more energy than smaller ones, which can have implications in fields such as acoustics and fluid dynamics.
In summary, Lighthill's Eighth Power Law states that the collective energy of a group of swimmers or sounds is proportional to the eighth power of their number. This means that larger groups can create much more energy than smaller ones, which can have implications in various fields.
Now, let's take a moment to imagine that we are standing outside, and we hear a sound. We can tell how loud it is by measuring its intensity or the strength of the sound waves reaching our ears. This intensity or energy is also directly proportional to the sound's perceived loudness, meaning louder sounds have a greater energy than softer ones.
But what happens when we have a group of swimmers or a group of sounds coming towards us? Based on our previous experiences with waves and sound, we might think that the collective energy of the group is just the sum of each individual's energy. However, that's not the case.
Here's where Lighthill's Eighth Power Law comes in. According to this law, the collective energy of a group of swimmers or sounds is actually proportional to the eighth power of their number. That might sound complicated, but let's break it down.
Imagine you have two swimmers. According to Lighthill's Eighth Power Law, the collective energy they create by their movements is proportional to 2^8, or 256. If you have three swimmers, the collective energy increases to 3^8, or 6,561. And if you have ten swimmers, the energy increases to 10^8, or 100,000,000.
Similarly, if you have two sounds, the collective energy they create is proportional to 2^8 or 256. If you have three sounds, the collective energy increases to 3^8 or 6,561. And if you have ten sounds, the energy increases to 10^8 or 100,000,000.
This exponential increase in energy means that we can't just add up the energy of each individual to get the total collective energy. It also suggests that larger groups can create much more energy than smaller ones, which can have implications in fields such as acoustics and fluid dynamics.
In summary, Lighthill's Eighth Power Law states that the collective energy of a group of swimmers or sounds is proportional to the eighth power of their number. This means that larger groups can create much more energy than smaller ones, which can have implications in various fields.