When we deal with waves, we're actually talking about couple of different types of movement. At its heart, a wave is a movement from one location to another location. It isn't the movement of one object, though. Instead, the molecules of the object all oscillate (move a little bit back and forth) to get the energy from point A to point B.

Transverse Waves

Transverse waves cause something to move or oscillate at a right angle of the direction of the wave's actual motion. Think: ocean waves. The maximum and minimum points are usually called the crest and trough. The distance the wave travels between a crest and a trough is half of a wavelength. One full wavelength is the distance from crest to crest or from trough to trough (doesn't matter which one you choose, just pick one and roll with it).

Want to see a transverse wave? Go jump into the ocean. No, really. Ocean waves travel across the ocean floor or shore, but the water also rises and falls perpendicular to the ocean floor. Next time you go surfing or visit your water park's wave pool, you can thank transverse waves for your mouth full of water.

Longitudinal Waves

If you're looking at a wave but the movement isn't perpendicular like that, you might be looking at a longitudinal wave. Longitudinal waves cause the material to move in the same direction of the wave. Basically, the wave moves by compressing and contracting (also known as a rarefying). When the molecules are closest together, they're compressed, and when they're farthest apart, they're contracted (rarefied). One example of a longitudinal wave is a sound wave, maybe you've heard about it?

 

With just a few compressions and contractions, you can go from quiet room to a folksy rendition of, "Empty Space." It's all thanks to longitudinal waves.
(Source)

Refraction

Let's back up a second. Before we can really figure out all the ifs, ands, and buts of longitudinal wave speeds, we need to know something about refraction. Refraction happens when light travels in anything that isn't a vacuum. If it's moving through any medium besides nothingness, there's a lot of stuff that gets in the way of a light particle's movement. Measuring the amount of stuff—also known as the optical density—keeping light from moving at the speed of…light, is known as finding the index of refraction.

It all has to do with Snell's Law. When a wave like light—or sound, for that matter—passes through something denser than a vacuum, we'll need to measure the change in the wave direction when it passes through that interface. We can measure all that by looking at the angle of the wave before and after it hits the new material.

The angle of incidence (the angle of the wave before it hits the interface) θ_i, and the angle of refraction θ_r (the angle of the wave when it's in the interface) are going to tell us just how much the wave changed when it hit a new material. Snell's Law gives a relationship between the angles, wave velocity, and wavelength in a function that looks something like this:

 

Surface Waves

The last wave type you'll need to know is the surface wave. This kind of wave travels along a surface between two media. If you've ever been in an earthquake, surfed the inside of an ocean wave, or blown across the surface of a cup of tea, then you've seen a surface wave. Surface waves are combinations of longitudinal and transverse waves that can form objects like vortices, air gaps, and standing waves.

Wavy Conclusions

All of these wave types can be sound waves and—more importantly—they all can be used by sonar technology. Because each type of wave has its own way of moving, it's going to give its own unique reflection for sonar to catch. When a sonar runs, it's going to pick up things like

• the temperature of the environment.
• the air pressure around the wave.
• the frequency.
• the amplitude.
• the period of repetition.
• the angle the sound wave was sent.
• tons of other things.

Each of these parameters, put together with the known mechanical properties of the "potential" wave (which is basically just an educated guess about what the wave should be), gives a sonar engineer the pieces to a giant jigsaw puzzle that need to be pieced together. Things can get complicated.

Quickly.