Cycle, Period, Amplitude, Frequency, Wavelength
Cycle: One complete repeat of the pattern/vibration
Period: The time required to complete one cycle. (unit is s)
Amplitude: The distance from the equilibrium position (resting position) to the maximum displacement when in motion.
Frequency: the reciprocal of period (unit is Hz: 1 Hz = 1 s -1).
Wavelength: the length of one complete wave cycle.
Longitudinal and Transverse Waves
A wave is a disturbance of a medium which transports energy through the medium without permanently transporting matter. In a wave, particles of the medium are temporarily displaced and then return to their original position. There are a variety of ways to categorize waves. One way to categorize waves is to say that there are longitudinal and transverse waves.
In a transverse wave, particles of the medium are displaced in a direction perpendicular to the direction of energy transport.
In a longitudinal wave, particles of the medium are displaced in a direction parallel to energy transport. The animation below depicts a longitudinal pulse in a medium.
The animation portrays a medium as a series of particles connected by springs. As one individual particle is disturbed, 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. In this type of wave - a longitudinal wave - the particles of the medium vibrate in a direction parallel to the direction of energy transport.
Wave & Energy
Much of what we see and hear is only possible because of vibrations and waves. We see the world around us because of light waves. And we hear the world around us because of sound waves.
A wave is a disturbance moving through a medium. There are two distinct objects in this phrase - the "wave" and the "medium." The medium could be water, air, or a slinky. These media are distinguished by their properties - the material they are made of and the physical properties of that material such as the density, the temperature, the elasticity, etc. Such physical properties describe the material itself, not the wave. On the other hand, waves are distinguished from each other by their properties - amplitude, wavelength, frequency, etc. These properties describe the wave, not the material through which the wave is moving.
A wave is an energy transport phenomenon that transports energy along a medium without transporting matter. A pulse or a wave is introduced into a slinky when a person holds the first coil and gives it a back-and-forth motion. This creates a disturbance within the medium; this disturbance subsequently travels from coil to coil, transporting energy as it moves. The energy is imparted to the medium by the person as he/she does work upon the first coil to give it kinetic energy. This energy is transferred from coil to coil until it arrives at the end of the slinky. If you were holding the opposite end of the slinky, then you would feel the energy as it reaches your end. In fact, a high energy pulse would likely do some rather noticeable work upon your hand upon reaching the end of the medium; the last coil of the medium would displace your hand in the same direction of motion of the coil. For the same reasons, a high energy ocean wave can do considerable damage to the rocks and piers along the shoreline when it crashes upon it.
Amplitude and energy
Over the course of time, the amplitude of a vibrating object tends to become less and less. The amplitude of motion is a reflection of the quantity of energy possessed by the vibrating object. An object vibrating with a relatively large amplitude has a relatively large amount of energy. Over time, some of this energy is lost due to damping. As the energy is lost, the amplitude decreases. If given enough time, the amplitude decreases to 0 as the object finally stops vibrating. At this point in time, it has lost all its energy.
If a slinky is stretched out in a horizontal direction and a transverse pulse is introduced into the slinky, the first coil is given an initial amount of displacement. The displacement is due to the force applied by the person upon the coil to displace it a given amount from rest. The more energy that the person puts into the pulse, the more work that he/she will do upon the first coil. The more work that is done upon the first coil, the more displacement that is given to it. The more displacement that is given to the first coil, the more amplitude that it will have. So in the end, the amplitude of a transverse pulse is related to the energy which that pulse transports through the medium. Putting a lot of energy into a transverse (or longitudinal) pulse will not affect the wavelength, the frequency or the speed of the pulse. The energy imparted to a pulse will only affect the amplitude of that pulse.
Consider two identical slinkies into which a pulse is introduced. If the same amount of energy is introduced into each slinky, then each pulse will have the same amplitude. But what if the slinkies are different? What if one is made of zinc and the other is made of copper? Will the amplitudes now be the same or different? If a pulse is introduced into two different slinkies by imparting the same amount of energy, then the amplitudes of the pulses will not necessarily be the same. In a situation such as this, the actual amplitude assumed by the pulse is dependent upon two types of factors: an inertial factor and an elastic factor. Two different materials have different mass densities. The imparting of energy to the first coil of a slinky is done by the application of a force to this coil. More massive slinkies have a greater inertia and thus tend to resist the force; this increased resistance by the greater mass tends to cause a reduction in the amplitude of the pulse. Different materials also have differing degrees of springiness or elasticity. A more elastic medium will tend to offer less resistance to the force and allow a greater amplitude pulse to travel through it; being less rigid (and therefore more elastic), the same force causes a greater amplitude.
The energy transported by a wave is directly proportional to the square of the amplitude of the wave. This energy-amplitude relationship is sometimes expressed in the following manner.
This means that a doubling of the amplitude of a wave is indicative of a quadrupling of the energy transported by the wave. A tripling of the amplitude of a wave is indicative of a nine-fold increase in the amount of energy transported by the wave. And a quadrupling of the amplitude of a wave is indicative of a 16-fold increase in the amount of energy transported by the wave.
To conclude: amplitude is the function of energy transported, inertial property of medium, and elastic property of medium.
Frequency and energy
At the same amplitude, waves of higher frequency transmit more energy per second than waves of lower frequency.
Relationship of Wave Speed, Wave Frequency, and Wavelength
The speed of an object refers to how fast an object is moving and is usually expressed as the distance traveled per time of travel. In the case of a wave, the speed is the distance traveled by a given point on the wave (such as a crest) in a given interval of time. In equation form,
If the crest of an ocean wave moves a distance of 20 meters in 10 seconds, then the speed of the ocean wave is 2.0 m/s. On the other hand, if the crest of an ocean wave moves a distance of 25 meters in 10 seconds (the same amount of time), then the speed of this ocean wave is 2.5 m/s. The faster wave travels a greater distance in the same amount of time.
Example: Noah stands 170 meters away from a steep canyon wall. He shouts and hears the echo of his voice one second later. What is the speed of the wave?
In this instance, the sound wave travels 340 meters in 1 second, so the speed of the wave is 340 m/s. Remember, when there is a reflection, the wave doubles its distance. In other words, the distance traveled by the sound wave in 1 second is equivalent to the 170 meters down to the canyon wall plus the 170 meters back from the canyon wall.
The speed of a wave is dependent upon frequency of the wave, and wavelength of the wave. A wave can vibrate back and forth very frequently, yet have a small speed; and a wave can vibrate back and forth with a low frequency, yet have a high speed. Frequency and speed are distinctly different quantities.
Wavelength of the wave is dependent upon the properties of the medium such as the tension of the rope.
Note: frequency of a wave does not depend on the medium. Instead, it depends on the source that produces the wave. When you produce a wave that goes from 1 medium to another, like the sound wave that goes from air to your ear, you will not see the frequency of the wave change. You will only see the wave length change and therefore the speed of the wave change.
To conclude: wave length is the function of the medium; frequency is the function of the wave-producing source; and speed of wave is the function of wave frequency and wave length.
Wave Equation
The speed of a wave is the product of the wavelength and the frequency.
Question: is it true that all waves of the same type in the same medium have the same speed?
The answer is yes. Waves of the same type have the same frequency; waves in the same medium have the same wavelength; from the "wave equation", we then know that the wave speed must then be the same.