Q: How do you think surface waves are related to transverse and longitudinal waves? A: A surface wave is combination of a transverse wave and a longitudinal wave. They differ in how particles of the medium move when the energy of the wave passes through. At the following URL, read the short introduction to waves and watch the animations. Then answer the questions below. The article gives a dictionary definition of wave. What is the most important part of this definition?
What happens to particles of the medium when a wave passes? What is the medium of a mechanical wave? List three types of mechanical waves.
If you shake one end of a rope up and down, a wave passes through the rope. Which type of wave is it? Can you guess what this picture shows? The objects are guitar strings, and the moving string is the one on the bottom right.
The string is moving because it has just been plucked. Plucking the string gave it energy , which is moving through the string in a mechanical wave. A mechanical wave is a wave that travels through matter.
The matter a mechanical wave travels through is called the medium. The type of mechanical wave passing through the vibrating guitar string is a transverse wave. A transverse wave is a wave in which particles of the medium vibrate at right angles, or perpendicular, to the direction that the wave travels. Another example of a transverse wave is the wave that passes through a rope with you shake one end of the rope up and down, as in the Figure below.
The direction of the wave is down the length of the rope away from the hand. The rope itself moves up and down as the wave passes through it. Q: When a guitar string is plucked, in what direction does the wave travel?
In what directions does the string vibrate? A: The wave travels down the string to the end. The string vibrates up and down at right angles to the direction of the wave. A transverse wave is characterized by the high and low points reached by particles of the medium as the wave passes through. The high points are called crests, and the low points are called troughs. You can see both in the Figure below. Transverse waves called S waves occur during earthquakes. The disturbance that causes an earthquake sends transverse waves through underground rocks in all directions away from the disturbance.
S waves may travel for hundreds of miles. An S wave is modeled in the Figure below. At the following URL, review transverse waves and watch the animations. Be sure to view the slow motion video of a transverse wave moving through a bungee cord. Give two examples of transverse waves.
How can you make a transverse wave in a Slinky spring toy? Based on the animation in the article, draw a sketch to show what happens to particles of the medium in a transverse wave. Include arrows to show the direction the particles move and the direction the wave travels. Sketch a transverse wave and label the crests and troughs. Infer how S waves might affect structures such as buildings. Pushing in on the end of a spring toy, for example, gives it energy that moves through the spring in a longitudinal wave.
A longitudinal wave is a type of mechanical wave. A mechanical wave is a wave that travels through matter, called the medium. Oscillatory motion is also important because oscillations can generate waves, which are of fundamental importance in physics. Many of the terms and equations we studied in the chapter on oscillations apply equally well to wave motion Figure.
Figure Although there are many versions, this one converts the up-and-down motion, as well as side-to-side motion, of the buoy into rotational motion in order to turn an electric generator, which stores the energy in batteries. A wave is a disturbance that propagates, or moves from the place it was created. There are three basic types of waves: mechanical waves, electromagnetic waves, and matter waves.
A medium is the substance a mechanical waves propagates through, and the medium produces an elastic restoring force when it is deformed. Mechanical waves transfer energy and momentum, without transferring mass. Some examples of mechanical waves are water waves, sound waves, and seismic waves. The medium for water waves is water; for sound waves, the medium is usually air. Sound waves can travel in other media as well; we will look at that in more detail in Sound. For surface water waves, the disturbance occurs on the surface of the water, perhaps created by a rock thrown into a pond or by a swimmer splashing the surface repeatedly.
For sound waves, the disturbance is a change in air pressure, perhaps created by the oscillating cone inside a speaker or a vibrating tuning fork. In both cases, the disturbance is the oscillation of the molecules of the fluid. In mechanical waves, energy and momentum transfer with the motion of the wave, whereas the mass oscillates around an equilibrium point. We discuss this in Energy and Power of a Wave. Seismic waves travel through the solids and liquids that form Earth.
In this chapter, we focus on mechanical waves. Electromagnetic waves are associated with oscillations in electric and magnetic fields and do not require a medium.
Examples include gamma rays, X-rays, ultraviolet waves, visible light, infrared waves, microwaves, and radio waves. Electromagnetic waves have some characteristics that are similar to mechanical waves; they are covered in more detail in Electromagnetic Waves in volume 2 of this text. Matter waves are a central part of the branch of physics known as quantum mechanics. These waves are associated with protons, electrons, neutrons, and other fundamental particles found in nature. The theory that all types of matter have wave-like properties was first proposed by Louis de Broglie in Matter waves are discussed in Photons and Matter Waves in the third volume of this text.
Mechanical waves exhibit characteristics common to all waves, such as amplitude, wavelength, period, frequency, and energy. All wave characteristics can be described by a small set of underlying principles. The simplest mechanical waves repeat themselves for several cycles and are associated with simple harmonic motion. These simple harmonic waves can be modeled using some combination of sine and cosine functions.
For example, consider the simplified surface water wave that moves across the surface of water as illustrated in Figure. Unlike complex ocean waves, in surface water waves, the medium, in this case water, moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. In Figure , the waves causes a seagull to move up and down in simple harmonic motion as the wave crests and troughs peaks and valleys pass under the bird.
The crest is the highest point of the wave, and the trough is the lowest part of the wave. The wavelength can be measured between any two similar points along the medium that have the same height and the same slope.
In Figure , the wavelength is shown measured between two crests. The amplitude of the wave A is a measure of the maximum displacement of the medium from its equilibrium position. In the figure, the equilibrium position is indicated by the dotted line, which is the height of the water if there were no waves moving through it. The units for the amplitude can be centimeters or meters, or any convenient unit of distance.
The amplitude A of the wave is the maximum displacement of the wave from the equilibrium position, which is indicated by the dotted line. In this example, the medium moves up and down, whereas the disturbance of the surface propagates parallel to the surface at a speed v. In equation form, this is. This fundamental relationship holds for all types of waves. For water waves, v is the speed of a surface wave; for sound, v is the speed of sound; and for visible light, v is the speed of light. We have seen that a simple mechanical wave consists of a periodic disturbance that propagates from one place to another through a medium.
In Figure a , the wave propagates in the horizontal direction, whereas the medium is disturbed in the vertical direction. Such a wave is called a transverse wave. In a transverse wave, the wave may propagate in any direction, but the disturbance of the medium is perpendicular to the direction of propagation. In contrast, in a longitudinal wave or compressional wave, the disturbance is parallel to the direction of propagation.
Figure b shows an example of a longitudinal wave. The size of the disturbance is its amplitude A and is completely independent of the speed of propagation v. Here, the spring moves vertically up and down, while the wave propagates horizontally to the right. In this case, the spring oscillates back and forth, while the wave propagates to the right. A simple graphical representation of a section of the spring shown in Figure b is shown in Figure.
Figure a shows the equilibrium position of the spring before any waves move down it. A point on the spring is marked with a blue dot. The disturbance of the wave is seen as the compressions and the expansions of the spring. Note that the blue dot oscillates around its equilibrium position a distance A , as the longitudinal wave moves in the positive x -direction with a constant speed.
The distance A is the amplitude of the wave. The y -position of the dot does not change as the wave moves through the spring. A periodic wave is a periodic disturbance that moves through a medium. The medium itself goes nowhere. The individual atoms and molecules in the medium oscillate about their equilibrium position, but their average position does not change. As they interact with their neighbors, they transfer some of their energy to them.
The neighboring atoms in turn transfer this energy to their neighbors down the line. In this way the energy is transported throughout the medium, without the transport of any matter.
The animation on the right portrays a medium as a series of particles connected by springs. As one individual particle is disturbed, and then returns to its initial position, it transmits the disturbance to the next interconnected particle. This disturbance continues to be passed on to the next particle. The result is that energy is transported from one end of the medium to the other end of the medium without the actual transport of matter. Each particle returns to its original position.
Periodic waves are characterized by a frequency , a wavelength , and by their speed. The wave frequency f is the oscillation frequency of the individual atoms or molecules. The speed v of the wave can be expressed in terms of these quantities. This relationship holds true for any periodic wave. If the individual atoms and molecules in the medium move with simple harmonic motion, the resulting periodic wave has a sinusoidal form.
We call it a harmonic wave or a sinusoidal wave. Problem : A wave on a rope is shown at some time t.
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