Waves Energy can be transported by transfer of matter. For example by a thrown object. Energy can also be transported by wave motion without the transfer of matter. For example by sound waves and electromagnetic waves.
Waves Mechanical waves travel through matter. The matter is referred to as a medium. Examples are sound eaves, waves on a string, and waves on water. Electromagnetic waves do not require a medium through which to travel. Examples are gamma rays, x- rays, ultraviolet light visible light etc.
Waves A wave is a disturbance or oscillation that travels through matter or space, accompanied by a transfer of energy.
Waves A transverse wave causes the medium particles to vibrate in the direction perpendicular to the motion of the wave.
Waves A longitudinal wave causes the medium particles to vibrate in the direction parallel to the motion of the wave.
Waves A pulse is a single disturbance travelling through a medium or space.
Figure 14-7 A Reflected Wave Pulse: Fixed End
Figure 14-8 A Reflected Wave Pulse: Free End
A crest is the point on a wave with the maximum value of upward displacement within a cycle.
A trough is the point on a wave with the minimum value of downward displacement within a cycle.
The amplitude is the value of the maximum or the minimum displacement from the average position
The wavelength (l) is the distance between corresponding points on consecutive waves. Unit: m
The frequency (f) is the number of waves that pass a given point per unit time. Unit: Hz=s -1
The speed of a wave is given by v=fl Unit: m/s
Figure 14-1 A Wave on a String
Waves A standing wave oscillates with time but appears to be fixed in its location
Figure 14-19 Wave superposition occurs when two or more waves meet in the same medium. The principle of superposition states that at the point where two or more waves meet the displacement of the medium equals the sum of the displacements of the individual waves.
Figure 14-20 The effect of two or more waves travelling through a medium is called interference. Constructive interference Destructive interference
Figure 14-20 Nodes and antinodes Nodes occur at points where two waves interact in such a way that the medium remains undisturbed. Antinodes occur at points where two waves interact in such a way that maximum displacement of the medium occurs.
Figure 14-20 Nodes and antinodes Antinode Node
Figure 14-20 Nodes and antinodes If one end of a string is attached to a vibrating object, and the other end is fixed, two wave trains are produced. One by the incident vibration, and one by reflection from the fixed end. The reflected wave train returns to the source and is reflected again. If the second reflection is in phase with the source, constructive and destructive interference will produce stationary antinodes and nodes. The string will appear to be vibrating in segments.
Figure 14-20 Nodes and antinodes This is called a standing wave an is an example of resonance.
String fixed at both ends
Figure 14-24b Harmonics
Figure 14-24c Harmonics
Reflection of Waves When a wave train strikes a barrier it is reflected. The law of reflection states that the angle of incidence is equal to the angle of reflection. The direction of the wave train s travel is called a ray, and the angles are measured from the normal to the boundary.
Reflection
Refraction of Waves When a wave train moves from one medium to another, its velocity changes. Since the waves in the new medium are produced by the waves in the old medium, their frequency remains the same. Since the velocity changes, but not the frequency, the wavelength must change.
Refraction of Waves When parallel waves approach a boundary between media along the normal, their direction does not change. When parallel waves approach a boundary between media at an angle to the normal, their direction is changed. This phenomenon is called refraction.
Refraction of Waves When parallel waves approach a boundary between media along the normal, their direction does not change. When parallel waves approach a boundary between media at an angle to the normal, their direction is changed. This phenomenon is called refraction.
Refraction of Waves Boundary
Refraction of Waves Boundary
Diffraction of Waves Diffraction is the bending of waves around obstacles in their path.
Diffraction of Waves
Diffraction of Waves
Diffraction of Waves An interference pattern can be created by placing a barrier with two openings in front of a wave train. The openings must be smaller than the wavelength of the approaching wave train.
Diffraction of Waves In regions where crests overlap with crests, and troughs overlap with troughs, constructive interference occurs, and antinodes lie along those lines. These lines are called antinodal lines. In regions where crests overlap with troughs destructive interference occurs, and the medium is undisturbed. These lines are called nodal lines.
Diffraction of Waves The pattern produced is called an interference pattern. Different wavelengths produce similar interference patterns, but the nodal and antinodal lines are in different places. Regardless of wavelength a central antinodal line always falls in the center of the pattern.
Standing waves on a string In order for standing waves to form on a string, the length of the string L must be a multiple of one half the wavelength l L n n 2 1, 2,3...
String fixed at both ends l 2L
Figure 14-24b Harmonics l L
Figure 14-24c Harmonics l 2 3 L
Speed of waves on a string F v= = mass length F the tension in the string
Speed of waves on a string Example A 4.0 m length of string has a mass of 20.00g. It is stretced between two points, and experiences a tension of 40.0N. The string is plucked. a) What is the velocity of a wave on the string? b)what is the longest wavelength possible for a standing wave on the string? c) What is the frequency of the longest wavelength possible for a standing wave on the string?
Speed of waves on a string Solution mass 0.02000kg 3 kg a) = 5.00 10 length 4.0m m F 40.0N m v= = =89.44 3 kg 5.00 10 s m
Speed of waves on a string Solution b)longest wavelength possible is l=2l l=2 4.0m 8.0m m 88.44 v c) v f f s l 11.055Hz l 8.0m