TRANSVERSE and LONGITUDINAL WAVESPage 5
Energy Travels by Waves
A wave is a disturbance that transfers energy through a medium by means of a series of vibrations. Energy is transmitted by means of a wave, but the medium through which the wave is traveling move along with the wave.
Transverse Waves
A transverse wave is one in which the vibrations are to the direction of travel of the wave. One example is provided by the waves that travel along the surface of water.
Since a wave actually consists of vibrating particles, the amplitude of a wave has the same meaning as it does for simple vibrations. The amplitude of a transverse wave is therefore the distance from the rest position to the top of a crest, or to the bottom of a trough. Although there is no common symbol to represent amplitude, we will use the symbol A. The wavelength is the distance required for one complete wave. (i.e. From one crest to another.) To represent wavelength we use the Greek letter lambda,λ. If we could freeze a transverse wave in time, it would appear as shown below.
Each of the points along the wave is vibrating up and down, but is not moving along the axis. As a result of these vibrations, the wave consists of regions that are above and others that are below . Regions above the rest position are called crests while those below are called troughs. Point k is on the backside of a crest and is therefore moving downward just like point S. Point W on the other hand is on the front side of a trough and is therefore moving up.
It is apparent, then, that any point on the leading side of a crest moves upward, and any point on the trailing side of a crest moves downward. , But what about points that are located at the top of a crest or at the bottom of a trough? Point T had been rising while the
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crest moved to the right. However, as the top of the crest passes by, the point will begin to drop. At the top of the crest, then, point T is neither moving upward nor downward. It is motionless. Similarly, a point at the bottom of a trough, such as X, is motionless for a brief instant of time.
Longitudinal Waves
In the case of a longitudinal wave, the particles of the medium vibrate back and forth to the direction in which the wave is traveling. The image below portrays a longitudinal wave. In this diagram, the vertical lines represent the coils in a slinky spring.
Because the coils are vibrating parallel to the direction of travel, from time to time they move closer to each other than normal. This creates a region called a . At other times the coils move farther from each other, forming a .
You will notice that the amplitude of the longitudinal wave has not been marked. Although we can deduce the amplitude from this diagram, it is not a measurement that can be easily indicated since the rest position is difficult to label on the diagram. You can however, see the wavelength labeled as λ.
THE UNIVERSAL WAVE EQUATION
The universal wave equation works for all waves regardless of the medium that the wave is traveling in. It is:
Where:
Eg.Determine the speed ofawater wave that has a wavelength of l0.0mand a frequency of 0.25 Hz.
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Name:
Questions:
Use this picture for question 1 and 2.
1. What direction are points A, B, C, D, and E moving?
2. What point is in phase with point C?
3. Calculate the speed of a wave that has a wavelength of 34 m and a frequency of 2.5 Hz.
4. Calculate the frequency of a water wave that has a speed of 4.00 m/s and a wavelength of 3.00 m.
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5. A light wave has a frequency of 5.0 x 1014 Hz and a speed of 3.0 x 108 m/s. Calculate its wavelength.
6. An earthquake wave travels at 4.0 km/s. If its wavelength is 500.0 m,
what is its frequency?
7. A longitudinal sound wave in iron has a frequency of 10.0 kHz and a wavelength of 50.0 cm, How long will it take that wave to travel 15.0 m?