Wave Length Equation

Question

In the universal wave equation, what is a constant, as long as our wave medium stays the same? How can we create change in this value?

Referring to the previous question, what is the constant for sound (given a typical air situation)? What is the constant for light in air?

Answer 1

There are a few 'wave equations' but I am assuming by universal wave equation you are referring to

v = ƒλ and so I ask you, what does this equation mean? What hidden secrets are encoded in this equation?

v surely is velocity with units of m/s, ƒ is the frequency of the wave with units of Hz which is just fancy for 1/s read as per second, and λ is the wave length of a wave measured in units of distance so like meters and such.

So mathematically this equation represents a basic fundamental relationship between velocity, frequency, and the wavelength of a wave because you can notice if we play around with the units we receive:

m/s = 1/s * m which is valid.

So, a long time ago or so, I don't know when, some physicist dude was observing the behavior of waves and just threw together a formula that calculates velocity, but now there must be implications that furthers a true tangible meaning of this equation which are really the questions you asked and I am taking a long time to give the answer to. Here's the answer:

velocity as described in this equation has limits of the medium in which the wave travels. A wave is just a propagation of energy and it turns out that the speed of this propagation is based on the medium. Thats all to say that light travels at roughly 3*10^8 m/s in a vacuum and sound travels at around 343 m/s in room temperature air this is constant Ill get to that more later. Now the frequency of a wave can change when you learn something called the Doppler affect, but really just like if you sit by a pool of water and push the water outwards, the waves will not change in frequency, so frequency can be thought of as constant. And this makes sense because if you think of frequency being the movement of wavefront in order for a change in frequency the wavefront must be traveling faster which violates what we established before that velocity of a medium is constant. Now the wavelength is really just dependent of the frequency and so if frequency is constant because velocity is constant than so is wavelength.

Now, the speed of light is a constant in a vacuum and some say that it slows down in different mediums, but that is a bit hard to visualize why, so lets think of sound waves. Air is a bunch of molecules that constantly bounce off each other and this bouncing transfers energy. Sound is really just the bouncing of air molecules. So when the temperature changes so does the density of the air or rather how tight each air molecule is. So when its cold the air is denser so sound should travel faster because the molecules are bouncing off each other quicker because there is a shorter distance between each molecule.

SO this is the short answer here is:

velocity is constant during specific conditions. You can change the velocity of a wave by enabling energy to flow faster or slower like with hot air the air molecules are farther away so the energy will flow slower. Frequency is really determined by the source meaning how fast you create the wave, like if you sit in a pool and splash fast youll create a wave with a high frequency. This changes based on the source. Wavelength is really just dependent on the frequency as well, because wavelength is really just the distance between two fronts.

I hope this helps. Physics is a philosophy that requires much thought and time and mathematics is the tool that models what we observe. It can get murky and confusing, but you must remember to think about it simply.

Take care and good luck.