March 24 – 27, 2015

What is a Wave?Watch the two waves.

What do you see?

How do the particles move?

Transverse wave

Longitudinal wave

The particles oscillate - they are NOT carried across the screen by the page.

KEY POINT: Waves carry ENERGY not MATTER

What is a Wave?Definition:

A wave is a disturbance that carries energy through matter or space without transferring matter.

The energy carried by a wave can be substantial – think of earthquakes, tsunamis, or the heat and light of the sun.

Transverse wave

Longitudinal wave

Transverse waveThe particles of the medium oscillate perpendicular to the direction of energy transfer/propagation of the wave. Examples:• earthquake secondary waves, • waves on a stringed musical instrument• waves on the rope, • EM waves: light, radio waves, microwaves…

Longitudinal waveThe particles of the medium oscillate parallel to the direction of energy transfer/propagation of the wave.

Creates areas of increased and decreased density• Areas of high density / pressure =

compression• Areas of low density / pressure = rarefaction

Examples• Sound waves• Earthquake p waves• Compression in a spring

Wavelength (λ) The length of one complete wave cycle of a wave measured in meters

Phase• Two points on a wave that occur in the same position within

the wave cycle – that is, they are one or more whole wavelengths apart -- are said to in phase.

• Points in a wave medium can be anywhere from 0° to 360° out of phase with each other.

• A trough and a crest are 180° out of phase with each other.

Wave characteristics

Amplitude, A

● the maximum displacement of a particle from its equilibrium

position.

● measured in m

● the greater the amplitude, the greater the energy of the wave

● if a wave doesn’t lose energy, then its amplitude remains constant; if the wave does lose energy then the amplitude decreases over time (damping)

Wave characteristics

Period, T ● is the time taken for one complete wave to pass any given point. ● measured in seconds

Frequency, f

● is the number of waves passing any given point per second. ● measured in cycles per seconds or Hz

1 1f = T =

T f

Wave characteristics

Wave speed, v

● The speed at which wavefronts pass a stationary observer. ● Depends only on the medium through which a wave travels!

Wave characteristics

Waves travel faster through material that is stiffer and through material that is less dense.

Speed of sound in:

air: 343 m/s helium: 1005 m/s water: 1500 m/s

bone: 3000 m/s steel rod: 5000 m/s

glass: 4500 m/s

Mechanical Waves

● Only propagate (transmit energy) through a medium ● Make the particles of the medium oscillate at frequency of the wave

Examples: waves on a string, sound waves, earthquakes, etc.,

EM (electromagnetic) waves ● Can propagate through a vacuum –or- through a medium ● Do not cause the particles of the medium to oscillate ● Made up of changing electric and magnetic fields ● always occur as transverse waves

● In a vacuum, EM waves travel at the speed of light c ≈ 3 x 108 m/s

(EM waves travel more slowly through a medium)

Mechanical vs. EM waves

A wave generator was used to generate waves of different frequencies in a rope. Two different tensions of rope where used. The wave speed and wavelength were measured.

Use the data in the table to answer the following questionsa) Which variable(s) affected wave speed?b) How are wavelength, frequency, and speed related?

Wave equation

a) Only tension (changing the stiffness of the medium) affects speed.

b) λ = (v/f) where, λ = wavelength, m v = wave speed, m/s f = frequency, Hertz (Hz)

Check your Understanding

Show:1)A arrives first2)B arrives first3)Same time4)Impossible to determine

Wave speed depends only on the medium!

Check your Understanding

c) Wave speed depends only on the medium!

Check your Understanding

2 seconds!

You do

A sound wave has a frequency of 192 Hz and travels the length of a football field, 91.4 m, in 0.271 s.

a) What is the speed of the wave?

b) What is the wavelength of the wave?

c) What is the period of the wave?

d) If the frequency were changed to 442 Hz, what would be the new wavelength and period?

a)v = x/t = 337 m/sb)λ = v/f = 1.76 mc)T = 1/f = 0.00521 sd)λ = v/f = 0.762 m; T = 1/f =

0.00226 s

You do

A sound wave produced by a clock chime is heard 515 m away 1.5 s later.

(a)What is the speed of sound in the air there? (b) The sound wave has a frequency of 436 Hz. What

is the period of the wave?

(c) What is the wave's wavelength?

You doA hiker shouts toward a vertical cliff 465 m away. The echo is

heard 2.75 s later.

(a) What is the speed of sound in air there? (b) The wavelength of the sound is 0.75 m. What is the

frequency of the wave? (c) What is its period?