# Mechanical Wave Characteristics

### After reading this section you will be able to do the following:

• Define periodic wave parameters like wavelength and period.
• Visualize periodic transverse waves and periodic longitudinal waves.

When the disturbance causing the transferse or longitudinal wave is repetitive (periodic), a periodic wave occurs.

### Periodic Transverse Wave

When periodic waves have simple harmonic motion they can also be called sinusoidal waves and any periodic wave can be described by a combination of sinusoidal waves.

As a sinusoidal wave travels each particle undergoes simple harmonic motion with the same frequency, but does not travel with the wave. It is important to distinguish between the particle motion and the wave motion since waves transport energy, but not matter. The figure below illustrates a traveling periodic transverse wave and points out different features of the wave like its wavelength and amplitude

The wavelength (represented by the Greek letter lambda) of a periodic wave is the physical distance between two same points in the pattern (e.g., the distance between two crests or the distance between two troughs). Since wavelength is a distance it is measured in distance units, typically meters. As a wave travels at a constant speed it advances 1 wavelength in the time of 1 period. The period of a wave, which is denoted by T, is measured in seconds and the wave speed, which is the speed the wave travels at in its medium denoted by v, is measured in meters per second. Frequency is the number of wave cycles that will pass a point in 1 second. It is measured in the unit Hertz (Hz).

$v={\lambda \over T}={\lambda f}$

${\lambda: wavelength}$

### Periodic Longitudinal Wave

Longitudinal waves can also be periodic. As a longitudinal wave travels there are regions of high particle density or pressure and regions of low particle density or pressure. These regions are called compression and rarefaction, respectively, and are shown in the figure below. Just like with a transverse periodic wave, a periodic longitudinal wave has a wavelength that is the physical distance between two same points in the pattern. In this case the wavelength can be defined as the distance between two compression regions or two rarefaction regions.

### Review:

1. When periodic waves have simple harmonic motion they can also be called sinusoidal waves.
2. Frequency is the inverse of the wave period and vice versa.
3. The wave speed is related to the wavelength and frequency of the wave.