Paul G Hewitt Conceptual Physics

Waves Wave: a periodic disturbance in a medium that carries energy, not matter, from one point to another.

Waves Most waves require a source and a medium of propagation. Medium: a substance or material that transmits the wave. Is composed of individual particles that interact with one another to carry the wave through the medium The particles themselves only vibrate in position-the wave transfers energy from one location to another.

Waves Two Types of Waves: I. Transverse wave: Particles of the medium move in a direction perpendicular to the direction the wave moves Examples: Light and other electromagnetic waves A vibrating string

Waves Parts of a transverse wave

Waves Amplitude: The maximum amount of displacement of a particle on the medium from its rest position

Waves Crest: The point on the medium that exhibits the maximum amount of positive or upward displacement from the rest position

Waves Trough: The point on the medium that exhibits the maximum amount of negative or downward displacement from the rest position

Waves Wavelength: The length of one complete wave cycle – The distance from crest to crest or trough to trough

Waves Frequency: how often particles of the medium vibrate when a wave passes through the medium number of complete vibrational cycles of a medium per a given amount of time unit for frequency is the Hertz (abbreviated Hz) where 1 Hz is equivalent to 1 cycle/second

Waves Amplitude: The amount of energy carried by a wave (is a disturbance in the medium) Energy is directly proportional to the square of the amplitude Energy imparted to initiate the wave only affects the amplitude Draw the parts of a transverse wave.

Waves Speed of waves: Remember speed = distance/time For a wave: speed = wavelength * frequency v = f * λ NOTE: the speed of a wave is not affected by any property of the wave itself – but by properties of the medium

Waves Examples: 1. What is the frequency of a wave that has a speed of 0.4 m/s and a wavelength of meter? m waves roll past you at a rate of 2 waves per second. Determine the wave speed.

Waves II. Longitudinal wave: Particles of the medium move in a direction parallel to the direction the wave moves Example: Sound waves

Waves Parts of a longitudinal wave: Compression – a point on a medium through which a longitudinal wave is traveling that has the maximum density Rarefaction – a point on a medium through which a longitudinal wave is traveling that has the minimum density

Waves Wavelength is the distance from compression to compression or rarefaction to rarefaction

Boundary Behavior I. Fixed End Reflection: One end of the medium is fixed at its boundary with another object. Reflected pulse is inverted. incident pulse: a pulse that is incident to or traveling towards (i.e., approaching) the boundary with the object reflected pulse: that part of the energy reflected and returned towards the wave origin. transmitted pulse: that part of the energy carried into the fixed object.

Fixed End Reflection At boundary: 1. the reflected pulse is inverted. (If an upward pulse is incident towards a fixed end boundary, it will reflect and return as a downward pulse.)

Free End Reflection B. One end of the medium is free to move at its boundary with another object. 1. The reflected pulse is NOT inverted.

Boundary Behavior The speed of the reflected pulse is the same as the speed of the incident pulse. The wavelength of the reflected pulse is the same as the wavelength of the incident pulse. The amplitude of the reflected pulse is less than the amplitude of the incident pulse.

Interference Wave interference Occurs when two waves meet while traveling along the same medium Constructive interference: The two interfering waves have a displacement in the same direction.

Interference Destructive interference: The two interfering waves have a displacement in the opposite direction

Interference Opposing waves have equal displacement:

Interference Opposing waves have unequal displacements:

Standing Wave Pattern Standing Wave Pattern: Pattern resulting from the presence of two waves of the same frequency with different directions of travel within the same medium Only occurs at certain frequencies These frequencies are called harmonics

Waves Nodes are points of no displacement (appear to be standing still) Antinodes are points of maximum displacement Nodes and antinodes are points on the medium that are staying in the same location. Crests and troughs are points of the disturbance that travel through the medium

Nodes and Antinodes

Reflection, Refraction, Diffraction Reflection: A change in direction of waves when they bounce off a barrier Refraction: A change in the direction of waves as they pass from one medium to another (the wave is “bent”) Diffraction: A change in direction of waves as they pass through an opening or around a barrier in their path

Law of Reflection The Law of Reflection: When a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.

Law of Reflection Point of incidence: where incident ray strikes a reflective surface Normal line: line perpendicular to the reflective surface Divides the angle between the incident ray and the reflected ray into two equal angles. Angle of incidence: between the incident ray and the normal line Angle of reflection: between the reflected ray and the normal line

Law of Reflection

Law of Refraction (Snell’s Law) n i sin Ɵ i = n r sin Ɵ r where Ɵ i = angle of incidence where Ɵ r = angle of refraction n i = index of refraction of the incident medium n r = index of refraction of the refractive medium Tells us how much a wave has been refracted

Incident and Refractive Angles

Snell’s Law Example Example: Carbon tetrachloride (n = 1.46) is poured into a container made of crown glass (n = 1.52). If the light ray in glass incident on the glass-to-liquid boundary makes an angle of 30° with the normal, what is the angle of the corresponding refracted ray with respect to the normal?

Snell’s Law Example Snell's law: n i sin Ɵ i = n r sin Ɵ r n i =1.52 (in glass) Ɵ i =30° (angle in glass) n r =1.46 (in carbon tetrachloride) sin Ɵ r =???

Snell’s Law Example 1.52 sin(30 ° ) = 1.46 sin Ɵ r [1.52 sin(30 ° )]/1.46 = sin Ɵ r = sin Ɵ r Ɵ r = sin -1 (0.5205) = 31.4 °

Mirrors Mirror: an optical device which has the capacity to reflect a beam of light and form a clear identical image Plane Mirror: the reflective surface of the mirror is in a single plane. Convex Mirror: the reflective surface of the mirror is the outside of a hollowed sphere Concave Mirror: the reflective surface of the mirror is the inside of a hollowed sphere

Images Real image: a real image is formed when all of the rays from a single point on an object strike a single point on the reflective surface The image is where light actually converges Virtual image: a virtual image is formed when rays of light appear to come from a real object, but there is in fact no object at the apparent source of the light. (the image is formed in a location where light does not actually reach) The image is where light appears to have converged

Mirror Equation A mirror equation can be used to determine the distance between a mirror and a reflected object. 1/f = 1/d o + 1/d i f = focal length d o = object distance d i = image distance Note: focal length is a measure of how strongly the system can bend light rays to bring an object into focus

Mirror Equation – Example I A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. Determine the image distance. 1/f = 1/d o + 1/d i (15.2 cm) = 1/(45.7 cm) + 1/d i cm -1 = cm /d i cm -1 = 1/d i d i = 22.8 cm The positive sign indicates the image is a real image

Mirror Equation – Example II A 4.0-cm tall light bulb is placed a distance of 8.3 cm from a concave mirror having a focal length of 15.2 cm. Determine the image distance. 1/f = 1/d o + 1/d i 1/(15.2 cm) = 1/(8.3 cm) + 1/d i cm -1 = cm /d i cm -1 = 1/d i d i = cm The negative sign always indicates the existence of a virtual image located behind the mirror

Mirror Equation – Example III A 4.0-cm tall light bulb is placed a distance of 35.5 cm from a convex mirror having a focal length of cm. Determine the image distance. 1/f = 1/d o + 1/d i 1/(-12.2 cm) = 1/(35.5 cm) + 1/d i cm -1 = cm /d i cm -1 = 1/d i d i = cm Convex mirrors always have a negative focal length (the focal point is behind the mirrors surface) The negative sign always indicates the existence of a virtual image located behind the mirror.

Doppler Effect The Doppler Effect: The effect produced by a moving source of waves in which there is an apparent upward shift in frequency for observers towards whom the source is approaching and an apparent downward shift in frequency for observers from whom the source is receding The effect is also noticed if the observer is moving.

Doppler Effect Example: A siren produces sound waves with a wavelength of 2m and a frequency of 5Hz. The boy will hear a frequency Above 5Hz while the girl will hear a frequency below 5Hz

Waves Pendulum: A mass, or bob, suspended from a fixed support that experiences simple harmonic (oscillatory) motion Oscillatory motion is: 1. the repeating variation in position around a central point 2. motion between two extremes around an equilibrium position

Waves Period: the length of time required for the pendulum to complete one back and forth swing. Period is measured as seconds/cycle T = 1/f T = period f = frequency