# Types of Waves

## Waves can exist perpendicular or parallel to their direction of travel through a material.

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Types of Waves

The period, \begin{align*}T\end{align*}, is the amount of time for the harmonic motion to repeat itself, or for the object to go one full cycle. In SHM, \begin{align*}T\end{align*} is the time it takes the object to return to its exact starting point and starting direction. The period of a wave depends on the period of oscillation of the object creating the wave.

The frequency, \begin{align*}f\end{align*}, is the number of cycles an object or wave goes through in 1 second. Frequency is measured in Hertz (Hz). 1 Hz = 1 cycle per sec.

The amplitude, \begin{align*}A\end{align*}, is the distance from the equilibrium (or center) point of motion to either its lowest or highest point (end points). The amplitude, therefore, is half of the total distance covered by the oscillating object. The amplitude can vary in harmonic motion but is constant in SHM. The amplitude of a wave often determines its strength or intensity; the exact meaning of "strength" depends on the type of wave. For example, a sound wave with a large amplitude is a loud sound and a light wave with a large amplitude is very bright.

A medium is the substance through which the wave travels. For example, water acts as the medium for ocean waves, while air molecules act as the medium for sound waves. When a wave passes through a medium, the medium is only temporarily disturbed. When an ocean wave travels from one side of the Mediterranean Sea to the other, no actual water molecules move this great distance. Only the disturbance propagates (moves) through the medium. An object oscillating with frequency \begin{align*}f\end{align*} will create waves which oscillate with the same frequency \begin{align*}f\end{align*}. The speed \begin{align*}v\end{align*} and wavelength \begin{align*}\lambda\end{align*} of a wave depend on the nature of the medium through which the wave travels.

There are two main types of waves we will consider: longitudinal and transverse waves.

In longitudinal waves, the vibrations of the medium are in the same direction as the wave motion. A classic example is a wave traveling down a line of standing dominoes: each domino will fall in the same direction as the motion of the wave. A more physical example is a sound wave. For sound waves, high and low pressure zones move both forward and backward as the wave moves through them.

In transverse waves, the vibrations of the medium are perpendicular to the direction of motion. A classic example is a wave created in a long rope: the wave travels from one end of the rope to the other, but the actual rope moves up and down, and not from left to right as the wave does. Water waves act as a mix of longitudinal and transverse waves. A typical water molecule pretty much moves in a circle when a wave passes through it.

Most wave media act like a series of connected oscillators. For instance, a rope can be thought of as a large number of masses (molecules) connected by springs (intermolecular forces). The speed of a wave through connected harmonic oscillators depends on the distance between them, the spring constant, and the mass. In this way, we can model wave media using the principles of simple harmonic motion. The speed of a wave on a string depends on the material the string is made of, as well as the tension in the string. This fact is why tightening a string on your violin or guitar will increase the frequency, or pitch, of the sound it produces.

### Review

1. Reread the difference between transverse and longitudinal waves. For each of the following types of waves, tell what type it is and why. (Include a sketch for each.)
1. sound waves
2. water waves in the wake of a boat
3. a vibrating string on a guitar
4. a swinging jump rope
5. the vibrating surface of a drum
6. the “wave” done by spectators at a sports event
7. slowly moving traffic jams
2. A mass is oscillating up and down on a spring. Below is a graph of its vertical position as a function of time.
1. Determine the
1. amplitude,
2. period and
3. frequency.
2. What is the amplitude at \begin{align*}t = 32\end{align*} seconds?
3. At what times is the mass momentarily at rest? How do you know?
4. Velocity is defined as change in position over time. Can you see that would be the slope of this graph? (slope = rise over run and in this case the ‘rise’ is position and the ‘run’ is time). Find the instantaneous speed at \begin{align*}t = 20\end{align*} sec.

1. a. longitudinal b. transverse c. transverse d. transverse e. transverse f. transverse g. longitudinal
2. a. i. 8 m ii. 20 s iii. 0.05 Hz  b. – 4 m  c. The mass is momentarily at rest at peaks (maximums) and valleys (minimums)  d. \begin{align*}\sim\end{align*} 2.3 m/s

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