Waves

1. A wave is a travelling disturbance
2. A wave carries energy from place to place

• A single disturbance that travels through a medium
• A wave of short duration

• If the disturbance repeats itself regularly then a periodic wave is generated.

• It is the disturbance that travels through the medium, not the medium itself.

• Regardless of the nature of the wave (sound, slinky, water, etc) or the medium through which it travels
(air, solid, liquid, etc.) all waves exhibit wave-like behaviour (interference, diffraction, refraction, etc.) and can be described using the same terminology
(amplitude, wavelength, speed, etc.) and the same mathematical equations
• When I use sound waves to demonstrate and illustrate the Doppler effect for example, it is not because only sound waves exhibit this effect. In fact all waves exhibit this effect. It’s just easiest to demonstrate it with sound waves.

• Two basic types of waves:
• If the disturbance is perpendicular to the direction of propagation of the wave it is called a transverse wave
• If the disturbance is parallel to the direction of propagation of the wave it is called a
longitudinal wave

trough crest

• Examples: pendulum, rocking chair, engine cycle, Earth’s orbit, etc.
• When talking about anything that repeats itself at regular time intervals we can define …
• The Period T: The time for one complete cycle
• The frequency f: The number of complete cycles per unit time
• What is the relationship between these two?

Period
24
1
1/7
1/365
Time Unit hours days weeks years
• Period and frequency are reciprocals
T

1 f f

1
T
Frequency
1/24
1
7
365

• The speed of a wave depends on the physical properties of the medium
• Examples:
– Waves travel faster through stiffer springs
– Speed of waves in water depends on the depth
– Sound waves travel faster in warmer air

• Fixed-end
• Free end

• Occurs at the boundary where the speed of wave changes

• What happens when two waves meet?
• Wave interference occurs when two waves act simultaneously on the same particles of a medium.
There are two types of interference: constructive and destructive.
• destructive interference occurs when a crest meets a trough resulting in a lower amplitude
• Constructive interference occurs when pulses build each other up, resulting in a larger amplitude (crest meets a crest or trough meets a trough)

• Longitudinal wave that is created by a vibrating object
• Sound wave consists of traveling pulses of high pressure zones, or condensations, alternating with travelling pulses of low pressure zones, or rarefactions
• These pressure fluctuations are normally very small

• Sound requires a medium ( gas , liquid, or solid )
• Cannot exist in a vacuum

• A sound with a single frequency is called a pure tone
• Human hearing
– You can hear sounds from 20 Hz to 20000 Hz (20 kHz)
– Me…up to about 12 -14 kHz
– Infrasonic (<20 Hz) Ultrasonic (>20 kHz)
– Rhinos use infrasonic (down to 5 Hz)
– Bats use ultrasonic (up to 100 kHz)
• The brain interprets the frequency detected by the ear in terms of pitch

• High pitch corresponds to high frequency
• Low pitch corresponds to low frequency

• Sound travels through gases, liquids, and solids, at considerably different speeds
• At room temp in air its approx 343 m/s
• Moves 4 times faster in water
• Moves 17 times faster in solids
• Speed increases with temp
– Air (0°C) 331 m/s
– Air (20°C) 343 m/s

• Unless otherwise stated assume air at 20°C

• Nearly all objects when hit, struck, plucked, or strummed will vibrate
• They tend to vibrate at a particular frequency
(or set of frequencies) called the natural frequency
• Some tend to vibrate at a single frequency
(pure tone) like a flute or a tuning fork while others vibrate at a set of frequencies

• The natural frequency of an object is determined by its physical properties
• Example: Guitar String
– Linear density
– Tension
– Length

Flute
• 200 Hz
Tuba
• 200 Hz
• 400 Hz
• 600 Hz
• 800 Hz
• 1000 Hz
Dropped Pencil
• 197 Hz
• 211 Hz
• 217 Hz
• 219 Hz
• 287 Hz
• 311 Hz
• 329 Hz
• 399 Hz

• The tendency of one vibrating object to force another object into vibrational motion
• A louder sound is always produced when an accompanying object of greater surface area is forced into vibration
• Examples
– Wooden body of a guitar
– Sounding board in a piano

• Occurs when the frequency of forced vibration matches the natural frequency of the second object
• The result is always a large vibration

• Sound waves, like any waves, can be made to exhibit interference
• When two or more sound waves from different sources are present at the same time, they interact with each other to produce a new wave.
• The new wave is the sum of all the different waves.

• Wave interaction is called interference.
• If the compressions and the rarefactions of the two waves line up, they strengthen each other and create a wave with a higher intensity.
• This type of interference is known as
constructive.
• When the compressions and rarefactions are out of phase, their interaction creates a wave with a dampened or lower intensity.
• This is destructive interference.

• A special case of interference occurs when two tones of slightly different frequencies are sounded together
• A fluctuation in the loudness, called beats, is heard
• The frequency of the beats is equal to the difference in frequencies
• Example: If a 262 Hz and 266 Hz tuning forks are sounded together the beat frequency will be …
• … 4 Hz !!!!

• the bending of waves around obstacles and the spreading out of waves beyond openings.
• Most pronounced when the wavelength is comparable to the size of the opening or obstacle

• is the change in frequency of a wave for an observer moving relative to the source of the wave.
• It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from an observer.
• The received frequency is higher (compared to the emitted frequency) during the approach, it is identical at the instant of passing by, and it is lower during the recession.

• Particle or wave?
• Up until 1801 there were two competing theories –light as a wave and light as a particle
• Both theories could explain the then known properties of light, namely reflection and refraction

• Showed that light was a wave

• In 1865 he proposed the existence of electromagnetic waves produced by the vibration of electric charges
• When he calculated the speed at which such waves should propagate it came out to a value very close to that of the speed of light
• He concluded that light was a form of electromagnetic radiation

• Albert Einstein (1905) explained the photoelectric effect by theorizing that light is composed of particles whose energy depended on the frequency of the light
• He called these particles photons

• Electromagnetic radiation propagates following linear wave equations, but can only be emitted or absorbed as discrete elements, thus acting as a wave and a particle simultaneously.
• In 1924, Louis-Victor de Broglie formulated the de
Broglie hypothesis, claiming that all matter, not just light, has a wave-like nature
• This was confirmed 3 years later when electrons were observed to behave like waves and form interference patterns

• Ole Romer first demonstrated in 1676 that light travelled at a finite speed (as opposed to instantaneously)
• First accurate measurement was made in 1880 by
Albert Michelson
• The speed of light in vacuum, usually denoted by
c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second c

3 .
0

10
8 m / s

• Refraction is the change in direction of a wave due to a change in its speed.

n
 c v

• Light emitted by a common lamp has many different frequencies and it tends to spread out after a short distance becoming wider and wider and less intense with increased distance
• It is said to be incoherent
• A beam of light that has the same frequency and direction is said to be coherent
• Coherent light is produced by a laser

• A laser emits a coherent light beam with a wavelength of 650 nm. What is the frequency of the wave?

n=4 fourth order n=3 third order n=2 second order n=1 first order n=o central bright n=1 first order n=2 second order n=3 third order n=4 fourth order

• http://www.acoustics.salford.ac.uk/feschools/ index.htm
• http://www.acoustics.salford.ac.uk/feschools/ waves/flash/huygens.swf