Waves Review

Ch13 (p408-433)

Ch14(all)

OverviewWaves are created when a periodic disturbance propagates outwards,

transmitting energy (but not matter).

Five wave properties:1. Speed (v, m/s): Determined by the elastic and inertial properties of the

medium. v=d/t v=f=/T2. Frequency (f, Hz): Cycles per second. Determined by the oscillating

source of the wave. 3. Period (T, s): Seconds per cycle. How much time ti takes for wave

motion to repeat. The reciprocal of frequency.4. Wavelength (, m): Distance between two identical points on a wave.

(eg. From crest to crest).5. Amplitude: Size of wave disturbance. Half the distance from peak to

crest.

Classifications (recognize and give examples of each)Mechanical vs. ElectromagneticPulsed vs. ContinuousTransverse vs. LongitudinalTraveling vs. Standing

OscillatorsSprings:

|Fsp|=|kx| Usp= ½ kx2 T=2(m/k)½

Energy is conserved so: ½ kx2 + ½ mv2 = constant

= ½ kA2

Pendulums:T=2(L/g)½

Change of direction

Reflection: Incident wave bounces back from interface (incident=reflection)

Diffraction: Wave curves around a barrier or spreads out when passing through an opening (no change of medium)

Refraction: Incident wave is bent as it is transmitted across an interface (Snell’s Law)

Wave interferenceLaw of superposition: when two waves coincide their amplitudes are

added

Constructive interference: when two waves are “in sync” their amplitudes combine

Destructive interference: when crests of one wave coincide with troughs of other they cancel out

Examples: • Standing waves and resonance• Beats• Double slit interference• Single slit diffraction• Thin film interference

Standing waves

• String fixed on each end, or tube open on each end:

1 = 2L, n=1/n n=1,2,3,4,….

f1 = v/2L fn=nf1

• Tube closed on one end

1 = 4L n=1/n n=1,3,5,7….

f1=v/4L fn=nf1

Beats

When waves of slightly different frequency go in and out of sync they cycle between constructive and destructive interference which results in a periodic variation in their amplitude

Fbeat=|f1-f2|

Double slit interferenceRequirements:• Incident waves should be monochromatic (single wavelength) & coherent

(arrive at each slit “in sync”)• Slits should be small enough to cause waves to diffract (and spread out)• Different path lengths mean that waves arriving from each slit may or may not

be in sync.

Condition for constructive interference:x=nn=1,2,3…)

Double slit interference results in constructive interference when:dsin=nor yn=nL/d

Single slit diffraction results in destructive interference when:asin=n or yn=nL/a

Bragg scattering (x-rays!) results in constructive interference when:2dsin=n

Doppler effectWhen source and observer are in relative motion toward one another

the wavelength is decreased, and the frequency is increased (ambulance approaching)

When source and observer are in relative motion away from one another the wavelength is increased, and the frequency in decreased (ambulance receding)

For sound waves this caused the PITCH to shift up (toward) or down (away).

For light (EM) waves this causes the COLOR to shift blue (toward) or red (away)

Doppler has nothing to do with amplitude and what matters is relative motion NOT proximity

f’ = f (v+vo)/(v-vs) for motion toward (reverse signs for motion apart

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave

Explain what each symbol in the formula yn=nL/d stands for and when this formula might be used

Formula used for double slit Formula used for double slit interference when the screen is interference when the screen is far (L>>d from the slits)far (L>>d from the slits)=wavelengthd=distance between the openingsL=distance from the slits to the screenYn=distance on screen to interference peekn=an integer

Because particles of air move back in forth in the direction that a sound wave is travelling, sound must be a _______.

Longitudinal waveLongitudinal wave

Wave property that depends on the medium the wave is traveling through.

Wave speedWave speed

The change in pitch heard as an ice cream truck approaches and then recedes is an example of ______.

The Doppler EffectThe Doppler Effect

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave

The ______ of a wave does not change as it enters a new medium.

A) Speed C) directionB) Wavelength D) frequency

D) frequencyD) frequency

The formula for spring potential energy is:

U=½kxU=½kx22

The bending of a wave as it enters a new medium is called______:

RefractionRefraction

A wave that completes 30 oscillations in one minute has a period of ___ s, a frequency of ____ Hz.

2.0 seconds, 0.5 Hz2.0 seconds, 0.5 Hz

A sound wave traveling at a speed of 340 m/s has a wavelength of 1.7 meters. What is its frequency?

200 Hz200 Hz

A 42.5 cm long tube is open on both ends. What is the fundamental resonant frequency if the speed of sound is 340 m/s? What are the next two harmonics for this tube?

ff11=v/2L=340/0.85=400Hz=v/2L=340/0.85=400Hzff22=2f1=800 Hz, f=2f1=800 Hz, f33=1200 hz=1200 hz

An astrophysicist observes a distant galaxy moving away from us. Due to the galaxy’s motion its light would:

a) Shift toward red end of spectrumb) Shift toward blue end of spectrumc) Take longer to reach usd) Have a longer wavelength and a smaller frequency.

Both a and d are correct!!Both a and d are correct!!

A 1.2 meter long organ pipe is closed on one end. Its fundamental frequency is 72.9 Hz. Determine the next two harmonics, and the speed of sound.

ff33=3f=3f11=219 Hz f=219 Hz f55=365Hz=365Hz11=4L=4.8m v==4L=4.8m v=11ff11=350 =350 m/sm/s

The period of spring oscillation is given by the formula:

T=2T=2(m/k)(m/k)½½

The period of oscillation for a simple pendulum is given by the formula:

T=2T=2(L/g)(L/g)½½

A 2.0 kg mass hanging from a spring is in static equilibrium when the spring stretches by 80 cm. What is the spring constant?

Fsp – Fg = 0Fsp – Fg = 0kx = mgkx = mgk = mg/x = 20/.8 = 25 N/mk = mg/x = 20/.8 = 25 N/m

List the parts of the electromagnetic spectrum from longest wavelength to shortest.

Radio,micro,IR,VIS,UV,x-Radio,micro,IR,VIS,UV,x-ray, gammaray, gamma

What is the speed of a radio wave?

3x103x1088m/s (same for all EM m/s (same for all EM waves in air or vacuum)waves in air or vacuum)

400 nm light strikes two narrow slits that are separated by 0.40 mm. A screen is located 2.0 meters away. How far apart will the bright lines be located? How would their separation change if the slits were further apart?

YYnn=n=nL/dL/dYY11=4x10=4x10-7-7x2/4x10x2/4x10-4-4=2mm (since this is the distance =2mm (since this is the distance from central maximum we have answered the from central maximum we have answered the question)question)

There is an inverse relation between yn and d, so There is an inverse relation between yn and d, so moving the slits further would make the bright lines moving the slits further would make the bright lines closer to one another)closer to one another)

A 3.0 kg bob oscillates 40 times per minute at the end of string. How long is the string?

F=40/60=2/3 hz T=1/f=1.5 F=40/60=2/3 hz T=1/f=1.5 ssT=2T=2(L/g)(L/g)1/21/2

L=(gTL=(gT22)/(4)/(422)= 57 cm)= 57 cm

A plucked guitar string is an example of a… (standing/traveling), (transverse/longitudinal), (mechanical/EM) wave

Standing, transverse, Standing, transverse, mechanicalmechanical

A wave that does not require a physical medium to travel through is an ______ wave.

Electromagnetic waveElectromagnetic wave

The boundary between two media is called an ______.

interfaceinterface

Write the formula for the Doppler effect and explain what each term means.

f’=f(v+vf’=f(v+voo)/(v-v)/(v-vss))

f=original frequency of the soundf=original frequency of the soundv=speed of the soundv=speed of the soundvvoo = speed of the observer (relative to = speed of the observer (relative to the air)the air)vvss = speed of the source (relative to the = speed of the source (relative to the air)air)f’ = the doppler shifted frequency heard f’ = the doppler shifted frequency heard by the observerby the observer

Algebraic signs given are for relative Algebraic signs given are for relative motion motion towardtoward one another one another

A stereo is blasting a 660 Hz pitch from a car that is traveling away from you at 20 m/s. (use vsound = 343 m/s)

a) Is the pitch you hear higher or lower than that heard by the person in the car?

b) What is the frequency of the sound that you detect?

Pitch is Pitch is LOWER.LOWER.f’=f(v+vo)/(v-vs)=660(343)/(363)=624 Hzf’=f(v+vo)/(v-vs)=660(343)/(363)=624 Hz

Note the change of sign…using the negative would Note the change of sign…using the negative would have given us a HIGHER pitch which is WRONG!!have given us a HIGHER pitch which is WRONG!!

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave

A wave that requires a physical medium to travel through

Mechanical waveMechanical wave