Transverse Waves

What happens when a stone is thrown on the water? What do you feel while sitting on a boat as the boatman is paddling in the water? The paperboat is moving up and down to a distance in the pond. The lilies move as the frog jump off them. Any disturbance on the water produces waves which travels through a medium and carries energy which may affect the motion of the body in contact with the water surface. When a stone is thrown on the water, ripples appear and will make some objects in the water move. You sway with the boat because of the waves in the sea. Waves are produced as the frog jump off a lilypad making the other lilies move.

Waves is classified as to how it moves in a medium. The direction of the force which causes the wave affects the direction of the wave. Transverse wave travels in up and down motion - the highest point is called crest and the lowest point is the trough. It can be measured by its amplitude and wavelength. Amplitude is the height of the crest or the trough. Wavelength is the distance from crest to crest or from trough to trough.

A wave is described according to its speed expressed as

\(v=\frac {\lambda}{T}\)                           (1)

where \(v\) is the speed of the wave in meter per second, \(m/s\)\(\lambda\) is the wavelength or the distance covered by the wave in meter, \(m\) and \(T\) is the period or time when the wave travels in second, \(s\).

Since the period varies inversely as the frequency of the wave \(f\) in Hertz, \(Hz\), (1) can be written as

\(v=\frac{\lambda}{\frac 1f}=\lambda f \)                   (2)

Frequency is the number of waves per second, thus it is also expressed in the unit per second, \(/s\).


Example 1.

A boy is caught by a traffic policeman, jaywalking. If the frequency of the policeman's whistle is \(1,000\; Hz\), solve for the wavelength of the sound produced by the whistle given that the speed of sound in air is \(344\;m/s\).

Given:

\(f=1,000\;Hz\\ v=344\;m/s\)

Solution:

Using equation (2), the wavelength is

\(\lambda=\frac vf=\frac {344\;m/s}{1,000/s}=0.344\;m\).


Example 2.

Elle is playing a paperboat. Calculate the time the wave travels if the boat is traveling at \(2\;m/s\) and the distance from crest to crest is \(0.5\;m\).

Given:

\(v=2\;m/s\\ \lambda=0.5\;m\)

Solution:

Using formula (1), the time or period of the wave is

\(T=\frac{\lambda}{v}=\frac{0.5\;m}{2\;m/s}=0.25\;s\).