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.