A shaking rope is a good example of a transverse wave. The wave moves along the rope but the bits of rope go up and down - across the direction of the wave. “Trans” means across, think of “transatlantic” or “transfer”. Most of the examples of waves we have to deal with are transverse waves. All the waves in the electromagnet spectrum are transverse waves.
A water wave is another example of a transverse wave.
A longitudinal wave
is a “pushing” wave. A line of dominos falling is an example although not a real practical example. Another way to illustrate a longitudinal wave is with a slinky spring. If one end of a slinky is pushed and pulled then each coil pushes and pulls the next. The coils oscillate along in the same direction that the wave is traveling. Proper practical examples of longitudinal waves are sound and the electrons in a wire transmitting an alternating current.
Measurements on transverse and longitudinal waves waves
a is the amplitude of the wave measured from the maximum height to the middle or from the trough to the middle. Measured in metres. Think of a water wave, it is the distance from either the crest or the trough to where the water would be if it were calm. The height from the top of the crest to the bottom of the trough is twice the amplitude. The amplitude of a longitudinal wave is much harder to show on a diagram. Think about the particles moving in a sound wave or the coils of a slinky spring. They oscillate backwards and forwards along the same line as the wave is travelling. The amplitude of the wave is the maximum distance the particle of air or the coil of the spring moves away from the mean or rest position.
λ is the wavelength, measured in metres. That is the distance from one point on a wave to the same point on the next wave - for example from crest to crest or trough to trough.
f is the frequency of the wave, that is the number of waves which are produced every second (or the number passing every second). This number is given the unit “hertz”. One hertz is one wave per second.
There is a connection between the frequency and wavelength of a wave. If the frequency is increased then there are far more waves and they are closer together. That means that the wavelength will be less. The speed of the wave overall is not affected by the frequency, but if we count all the waves produced in a second and measure the length of one then the total of wavelength times number will be the distance the first wave travelled in that second. That is the speed.
The speed is equal to the frequency multiplied by the wavelength.
A set of pdf notes on measuring waves is here:Measuring waves
There are more topics on the properties of waves, here: