CHAPTER FIVE
WAVES
What is a wave?
A wave is the propagation of a disturbance through a medium from
one point to another whereby the medium itself does not undergo
any net displacement attributable to the disturbance.
05/06/2023 1
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
study note on waves for physics stu
Typology: Study notes
2015/2016
1 / 52
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download physics study note on waves and more Study notes Physics in PDF only on Docsity!
CHAPTER FIVE
WAVES
What is a wave? A wave is the propagation of a disturbance through a medium from one point to another whereby the medium itself does not undergo any net displacement attributable to the disturbance.
This is seen in water waves which move from one point to another, but the water is not carried with it. This is also observed when a pebble is dropped into a pond. At the point where the pebble hits the water’s surface, waves are created. These waves move outward from the creation point in expanding circles until they reach the shore. If a leaf is made to float on the disturbed water and examined carefully, it will be observed that the leaf moves up, down and sideways about its original position but does not undergo any net displacement away from or towards the point where the pebble hit the water. The water molecules just beneath the leaf, as well as all the other water molecules on the pond’s surface, behave in the same way. Thus the water waves move from the point of origin to the shore, but the water is not carried with it.
A wave is either transverse or longitudinal. A transverse wave is a traveling wave that causes the particles of the disturbed medium to move perpendicular to the wave motion or velocity. Examples are water waves in a ripple tank, waves on plucked strings and electromagnetic waves. On the other hand a longitudinal wave is a traveling wave that causes the element of the disturbed medium to move parallel to the direction of motion. Examples are Sound waves and the waves generated by a vibrating spring along its axis.
Their disturbance corresponds to a series of high - and low- pressure regions (compressions and rare factions) that travel through air or any material medium with a certain speed. Every compressed region is followed by a stretched region.
Basic Definitions of Variables of Wave Motion Amplitude : Amplitude : This is the maximum displacement of a particle of the medium at its equilibrium position. It is denoted by A. Period : The time required for two identical points (such as crests) of adjacent waves to pass by a point. That is the time taken for one complete oscillation to be made. It is denoted by T. Frequency : This is the number of crests or troughs that pass a given point in a unit time interval. It is denoted by T f 1 Wavelength : This is the minimum distance between two crests or troughs on adjacent waves. It is denoted by λ Crest : The point at which the displacement of a medium from its normal level is highest.
Wavefront : this is a line or surface in the path of a wave motion on which the disturbance at every point have the same phase. These definitions can be used to derive an expression for the speed of waves. By definition, the speed of a wave is given as t x v . Where v is the speed at which a particular part of a wave, say crest, moves through a medium. Taking x and T t We have T v 5. Since the frequency is equal to the reciprocal of the period, we have v f
One consequence of the superposition principle is that two traveling waves can pass through each other without being destroyed or even altered. For example, when two pebbles are thrown into a pond and hit the surface at different places, the expanding circular surface waves do not destroy each other but rather pass through each other. The complex pattern that is observed can be viewed as two independent sets of expanding circles. Likewise, when sound waves from two sources move through air, they pass through each other. The resulting sound that one hears at a given point is the resultant of the two disturbances.
The combination of separate waves in the same region of space to produce a resultant wave is called interference. When the displacement caused by the two pulses is in the same direction, thus, in phase, their superposition is referred to as constructive interference but when the displacements caused by the two pulses are in the opposite direction, thus 180° out of phase, their superposition is said to be destructive interference.
Destructive interference If two waves y1 and y having the same frequency and amplitude are 180° out of phase, the resultant when they combine gives y and is a complete cancellation. It occurs when a crest of one wave arrives at the same time as a trough of the other wave. The amplitudes add up, but they are of opposite sign, so the total amplitude is reduced to zero.
Characteristics of Waves (Light) Light exhibits certain behaviors which are characteristics of any wave and would be difficult to explain with a purely particle- view. Light reflects in the same manner that any wave would reflect. Light refracts in the same manner any wave would refract. Light diffracts in the same manner that any wave would diffract. Light undergoes interference in the same manner that any wave would interfere. And light exhibits the Doppler Effect just as any wave would exhibit the Doppler Effect.
Reflection of waves All waves are known to undergo reflection or the bouncing off of an obstacle. Most people are very accustomed to the fact that light waves also undergo reflection. The reflection of light waves off a highly polished surface results in the formation of an image. One characteristics of wave reflection is that the angle at which the wave approaches a flat reflecting surface is equal to the angle at which the wave leaves the surface. This is observed for water and sound waves.
One application of reflection of sound waves is echo. In audio signal processing and acoustics, an echo is a reflection of sound, arriving at the listener some time after the direct sound. Typical examples are the echo produced by the bottom of a well, by the walls of an enclosed room. A true echo is a single reflection of the sound source. The time delay is the extra distance divided by the speed of sound.
An echo can also be explained as a wave that has been reflected by a discontinuity in the propagation medium and returns with sufficient magnitude and delay to be perceived. Echoes are reflected off walls or hard surfaces like mountains. When dealing with audible frequencies, the human ear cannot distinguish an echo from the original sound if the delay is less than 1/10 of a second. Thus, since the velocity of sound is approximately 343 m/s at a normal room temperature of about 20°C, the reflecting object must be more than 16.2 m from the sound source at this temperature for an echo to be heard by a person at the source.
The strength of echo is usually measured in dB sound pressure level (SPL) relative to the direct transmitted wave. Echoes may be desirable (as in sonar) or undesirable (as in telephone system). Uses of echoes
- Echoes are used in the exploration of oil
- They are also used in the determination of the depth of the sea.