Chapter 14 Waves and Energy Transfer
Types of Waves
• mechanical waves require a medium(water, air, springs)
• electromagnetic waves require no medium (light, radio, micro)
Types of Mechanical Waves Transverse - particles of the medium vibrate
perpendicular to the direction of the wave. eg. guitar strings
Longitudinal - particles of the medium vibrate parallel to the direction of the wave.
eg. sound waves
Wave pulse - a single disturbance that travels through a medium.
Wave train - a series of pulses at regular intervals (travelling wave).
Properties of a Wave
Period (T) - the time needed for one complete cycle or wave.
Frequency (Hz) - the number of complete cycles per second.
ƒ = 1 T = 1_
T ƒ
Wave Velocity
• the product of the frequency and the wavelength.
We know: v = d or v = λ
t T
But if T = 1/ƒ
Then by substitution:
v = ƒ λ v = velocity of the wave (m/s)
ƒ = frequency (Hz)
λ = wavelength (m)
Ex#1. The wavelength of a water wave is 0.55 m. If the frequency of the wave is 4.0 Hz, what is the speed of the wave?
v = ?
ƒ = 4.0 Hz
λ = 0.55 m
v = ƒ λ
= (4.0Hz)(0.55m)
= 2.2 m/s
Ex#2. A hiker on Mount Baker shouts across a valley to the other hillside, 750 m away. The echo is heard 4.4 s later. a) What is the speed of sound in air.
d = 2 x 750m = 1500m t = 4.4 s v = d t
= 1500m 4.4s
= 341 m/s
= 3.4x102 m/s
Ex#2. A hiker on Mount Baker shouts across a valley to the other hillside, 750 m away. The echo is heard 4.4 s later. b) The sound wave has a frequency of 436 Hz. What is its period?
f = 436 Hz
T = ?
T = 1/f
= 1/436 Hz
= 0.00229 s or 2.29x103 s
Ex#2. A hiker on Mount Baker shouts across a valley to the other hillside, 750 m away. The echo is heard 4.4 s later. c) What is the wavelength?
v = ƒ λ or λ = v
f
= 341 m/s
436 Hz
= 0.782 m/s
v = 341 m/s ƒ = 436 Hz λ = ?
DISCUSSION: WAVE VELOCITY
• Wave speed is dependent upon the medium. eg. spring tension, water depth
• If speed decreases, wavelength decreases (frequency remains constant).
• Frequency can only be changed at the source.
• If frequency increases, wavelength will decrease to maintain the same speed.
Amplitude of a Wave
• the amplitude of a wave is its maximum displacement from the rest position.
• in order to produce a wave with larger amplitude, more work has to be done.
Wave Interference • the speed of a mechanical wave depends upon
the medium.
eg. depth of the water, temperature of the air and spring tension.
• when the medium changes, wave energy is both reflected and transmitted.
• reflected waves: – from less dense to more dense -- inverted
– from dense to less dense – erect.
• waves passing from one medium to another have the same frequency.
Fixed End (Less dense to more dense): Reflected wave is inverted.
Free End (More dense to less dense):
Reflected wave is erect.
Superposition of Waves
• the resultant displacement of a particle caused by two or more waves.
• equal to the sum of the displacements produced by individual waves.
Constructive Interference
• troughs of the 2 waves occur at the same time; combined wave is larger than each of the separate waves.
Destructive Interference
• crests of one wave arrives at the same time as the troughs of the other wave; net amplitude is zero.
Partially Destructive Interference
• when 2 waves meet somewhere between the 2 extremes, or if waves have different amplitudes or different wavelengths.
Standing Waves
• when waves of identical wavelengths and amplitude interfere, a stationary interference pattern is produced.
• incident and reflected waves interfere in such a way that constructive and destructive interference occurs at fixed positions.
Nodes
• parts of the wave that remain stationary.
• points of complete destructive interference.
Antinodes
• positions with the largest amplitude.
• points of maximum constructive interference.
Reflection of Waves
Law of Reflection - angle of incidence is equal to the angle of reflection.
• reflected wave decreases in amplitude (waves lose energy due to friction and absorption by barrier).
Refraction
• waves change direction and wavelength at the boundary between 2 different media (ie. different depths of water)
• when waves enter shallow water:
a) frequency is the same(only changed at the source)
b) wavelength decreases
c) speed decreases
Diffraction
• the spreading of waves around the edge of a barrier.
• waves will bend as they pass through an opening or around an obstacle.
• greater wavelength = greater diffraction.
Doppler Shift
• change in frequency resulting from movement of wave source
i.e., change in pitch of ambulance siren as it approaches compared to when it moves away
• frequency of source doesn’t change, but the waves are compressed together as the source moves towards the receiver; therefore, the frequency of the detected wave is greater.