Properties of Plane Waves

Wavelength, Frequency and Velocity

As previously discussed, for mechanical waves among the properties of waves propagating in isotropic solid materials are wavelength, frequency, and velocity. The wavelength is directly proportional to the velocity of the wave and inversely proportional to the frequency of the wave. This relationship is shown by the following equation.

$$Wavelength(\lambda)=\frac{Velocity(\nu)}{Frequency(f)}$$

The applet below shows a longitudinal and transverse wave. The direction of wave propagation is from left to right and the movement of the lines indicate the direction of particle oscillation. The equation relating ultrasonic wavelength, frequency, and propagation velocity is included at the bottom of the applet in a reorganized form. The values for the wavelength, frequency, and wave velocity can be adjusted in the dialog boxes to see their effects on the wave. Note that the frequency value must be kept between 0.1 to 1 MHz (one million cycles per second) and the wave velocity must be between 0.1 and 0.7 cm/us.

As can be noted by the equation, a change in frequency will result in a change in wavelength. Change the frequency in the applet and view the resultant wavelength. At a frequency of .2 and a material velocity of 0.585 (longitudinal wave in steel) note the resulting wavelength. Adjust the material velocity to 0.480 (longitudinal wave in cast iron) and note the resulting wavelength. Increase the frequency to 0.8 and note the shortened wavelength in each material.

In ultrasonic testing, the shorter wavelength resulting from an increase in frequency will usually provide for the detection of smaller discontinuities. This will be discussed more in following sections.

Plane Wave

Plane waves are a special case of waves where a physical quantity, such as phase, is constant over a plane that is perpendicular to the direction of wave travel. There can be mechanical (both transverse and longitudinal) as well as EM plane waves. It should be noted that EM plane waves are only transverse. A visualization of a plane wave is shown below. Just like periodic waves, plane waves have a wavelength, frequency, and wave speed. 

When EM waves radiate from a source, such as an antenna, they radiate as spherical waves (see the figure below). As the waves move farther from the source, their energy gets spread out over a bigger spherical surface area. At big distances, which we call the far-field, a spherical wave front can be approximated as a uniform plane wave over a defined area.