WAVES
Definition
• What is Wave?
Wave is a method of propagation of energy
For example: when we drop a pebble into a pond of still water, a few
circular ripples move outwards, on the surface of the water. As these
circular ripples spread out, energy is being carried with them
• From definition above then waves carry energy.
For Example: during an earthquake, the seismic waves produced can
cause great damage to buildings and the surroundings
Source of waves
• The source of any wave is a vibration or oscillation
• Wave motion provides a mechanism for the transfer of energy from
one point to another without the physical transfer of the medium
between the two points.
Type of waves
• Remind: wave is method of propagation of energy
• Transverse wave: Energy propagate in a direction perpendicular to
the direction of vibration
Example: Rope waves, Water waves, Light waves, Radio waves,
Electromagnetic waves.
• Longitudinal wave: propagate in a direction parallel to the direction
of vibration.
Example: Sound waves and waves produced in a vertical oscillating
spring under tension.
Describing Waves
• Crest and troughs
• High point and low point that characterize transverse waves only. For
longitudinal wave, compression and rarefaction are used.
• Amplitude: The value of the maximum displacement from the rest of
central position in either direction.
• Wavelength: (λ) The shortest distance between any 2 points on a
wave that are in phase. The two easiest points to choose for a
distance of one wavelength are 2 successive crests or troughs.
• Frequency: (f : Hz) Number of completed waves produced per second.
For example: if the figure shows 2 completed waves and if they are
produced in one second then the frequency of this wave is 2Hz
• Period: (T : s) Time taken to product one completed wave.
• Wave speed: the distance travelled by wave in one second.
• Wave front: An imaginary line on a wave that join all points which are
in phase of vibration.
• Phase: 2 point are said to be in phase because that are moving in the same
direction with same speed and having same displacement from rest point.
Any 2 crests or troughs are in phases.
• Phase difference: is the difference, expressed in degrees or radians,
between two waves having the same frequency and referenced to the
same point in time
The wave equation and principle
• Speed = distance / time
• Wavelength is distance moved by the wave in one cycle i.e distance
• Time = period = 1/frequency
• So speed = wavelength / period
Wave speed on stretched string
Big wave rules:
• The speed of a wave is determined by the type of wave and
the characteristics of the medium, not by the frequency.
• When a wave passes into another medium, its speed changes, but
its frequency does not.
• What is medium?
Medium is environment that wave travel in.
Superposition principle
• Occurs when there is more than one wave in a medium at a given
time.
• At any instant, the resultant displacement is simply the sum of the
displacements of the individual waves.
• Constructive and destructive interference are obvious examples of
this idea.
• Constructive Interference: Resultant amplitude is larger than either individual
wave.
• Destructive Interference: Resultant amplitude is less than either individual
wave.
Examples
Constructive Interference:
Destructive Interference:
Constructive Interference
Standing Waves
…a wave in which the amplitude at a given location does not
vary with time.
Standing Wave Features:
• Amplitude is zero at fixed ends
• Nodes (other places with zero amplitude)
• Anti-nodes (places with maximum amplitude)
Standing Wave: Both Ends Fixed
Standing Wave: One End Fixed, One End Free
Reflection of Waves –
Fixed End
• Whenever a traveling wave
reaches a boundary, some or all
of the wave is reflected
• When it is reflected from a fixed
end, the wave is inverted
• The shape remains the same
Reflected Wave – Free End
• When a traveling wave reaches a
boundary, all or part of it is
reflected
• When reflected from a free end,
the pulse is not inverted
Mathematical Description of the Travelling waves
Or
Where:
- A : amplitude
- ω: angular frequency.
- λ: wavelength
y = A sin (ωt + 2πx/λ)
y = A sin (ωt - 2πx/ λ)
Sound wave
The speed of a sound wave depends on the medium through which it travels. In particular, it depends on the
density (ρ ) and on the bulk modulus (B), a measure of the medium’s response to compression.
• Sound level:
• Intensity: the rate at which they transmit energy, per unit area. (W/ 𝑚2 )
• Intensity is proportional with 𝐴2 => Intensity depends on the wave’s
amplitude: The greater the amplitude (A), the greater the intensity (and,
therefore, the louder the sound)
• Loudness: how soft or how intense the sound is as perceived by the ear and
interpreted by the brain. (Unit: decibels dB)
Where: 𝐼0 is threshold of hearing.
• Pitch : is perceived as how "low" or "high" a sound is and represents
the cyclic, repetitive nature of the vibrations that make up sound
(frequency)
• Duration: is perceived as how "long" or "short" a sound is and relates
to onset and offset signals created by nerve responses to sounds
• Beat: When two sound waves of different frequency approach your
ear, the alternating constructive and destructive interference causes
the sound to be alternatively soft and loud - a phenomenon which is
called "beating" or producing beats.
The Doppler effect is the way a wave seems to
increase or decrease in frequency when there is
relative motion between the observer and the
source of the wave.
Have you ever stopped at a railroad crossing to let
a train pass by? Did you notice that the sound of
the train's whistle is higher pitched when the train
was approaching and lower when it was
receeding? Then you have witnessed the Doppler
effect.
Doppler Acapella (Link)
When a source of waves and an observer are moving towards each other:
1. A higher frequency is heard
2. A shorter wavelength is observed.
When a source of waves and an observer are moving apart:
1. A lower frequency is heard
2. A longer wavelength is observed.
Doppler’s effect
Weather radars send out radio waves. Objects in the air, such as rain drops, snow
crystals, hail stones or even insects and dust, scatter or reflect some of the radio waves
back to the antenna. Weather radars electronically convert the reflected radio waves into
pictures showing the location and intensity of precipitation.
Doppler radars also measure the frequency change in returning radio waves. Waves
reflected by something moving away from the antenna change to a lower frequency.
Waves from an object moving toward the antenna change to a higher frequency.
Summary
• Type of waves:
W
AVES
M
echanical w
aves
Transversewaves
Electrom
agneticw
aves
Longitudinal waves
Transversewaves
Wave Properties - A wave is described in terms of the
following characteristics:
Amplitude
Wavelength ( )
Frequency (f )
Period (T)
Wave velocity (v)
Crest
Trough
Compression
Rarefaction
Nodes
Speed of wave
Constructive & Destructive Interference
Section 13.10