Physics, physical science
	Wave properties
	Surf’s up! The thrilling waves that challenge surfers have traveled hundreds or thousands of miles along the ocean. These waves can be described and better understood and then compared to other waves in our lives.

   There are two quite different but equivalent ways in which to measure the speed of a series of waves. Velocity is defined as the distance traveled divided by the elapsed time. v=d/t. A wave that has traveled 1 meter in 0.4 seconds has a velocity of 2.5 m/s.

We can look at this series of waves and describe certain properties. This will then lead us to another means of measuring the velocity. A wave is depicted below.

This depiction shows the wave at one point in time. In mathematics, we call this curve a sine wave. A few moments later, the wave will look like this:

As you can see, the entire wave has shifted to the right. The peaks (called crests) have moved to the right. The valleys (called troughs) have also moved to the right. The distance between the crests (equal to 1 wavelength and given the lambda symbol l) has remained the same. Similarly, the vertical disturbance distance (the amplitude A) has also remained the same.

If this wave were moving along a telephone cord or a slinky, you would recognize that the parts of the cord move up and down as the wave moves to the right. Imagine that a part of the telephone cord or slinky were painted red. The red part would move up and down as the wave passed, but the red part would not move to the right and be a different position from where it began.

In the wave depicted above, the wavelength is 1.0 meters. The amplitude is 5 centimeters. From the first two diagrams, drawn .02 seconds apart, we can see that it would takes a total of approximately 0.1 seconds to move to this position:

The wave must move for a total of 0.4 seconds to be in an identical position as the initial wave. Thus, the period of the wave is 0.4 seconds. The frequency of the wave is defined as the number of crests that pass a specific point in 1 second. In this case, the frequency would be 2.5 waves per second. The period of a wave and its frequency are a reciprocal relationship. f=1/T (where T is the period and f is the frequency.)

The speed of the wave is also equal to the frequency multiplied by the wavelength.

For the wave shown, the wavelength l is 1.0 meters, the frequency is 2.5 waves per second and the resulting velocity is 2.5 meters per second.

Water waves can travel at many different speeds depending on the depth of water. Sound waves travel at different speeds depending on the temperature of the air. A sound wave travels at approximately 340 m/s. This is equivalent to 3.5 football fields in 1 second. Light travels at 186,000 miles per second. This is such an incredibly fast speed that it is difficult to comprehend. More incredible is that it has been measured with increasing accuracy over the course of time.


a) Tsunamis are incredibly large waves caused by earthquake tremors that can wreak enormous damage when the 30-foot wave overwhelms a waterfront community. Research tsunamis, their creation, their frequency and the damage that have caused.
b) Measure the speed of sound. Have a friend stand at one end of a football field. As she reaches over her head to clap, you will see the hands come together before you hear them. Light takes virtually no time to get from you to her. Sound takes time. If you can measure that time, you will have a good measurement of the speed of sound.

What is this wave’s (a) amplitude and (b) wavelength. What else would be needed to calculate its speed? How could this be determined?