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As you enter… Pick up your quiz (sorted by section)

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Physics 7C SS1 Lecture 3: Interference

The reason for studying

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Agenda Review practice quiz Review Interference basics Review 1D interference (as studied in

DLM 4) Introduce 2D interference

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Which meets the quiz requirements better?

A

B

C: They are equally good

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Which meets the quiz requirements better?

C: They are equally good

B

A

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What is missing from this response?

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W 10 Gives clear instructions that could be carried out. • Wavelength, perhaps: measure the distance from one maximum to the

next maximum. This distance is the wavelength. • Period, perhaps: use the string to keep attention focused on one location.

Start time when the water is at a minimum value and stop time when the water next reaches a minimum value. The time recorded is the period. OR “record the time it takes for one peak to travel the distance of a wavelength to get the period.” OR “Find the frequency by measuring the amount of peaks that hit a certain point within a given amount of time, li ke 10 seconds, and divide the number counted by the time interval to get the number of cycles per second”

A 9.2 Proposed method is descriptive, but with a problem. • Wavelength: “ let string out beginning at a peak and stop at the next

peak.” The string would not actually travel with the wave’s disturbance. We have modeled the water as bobbing up and down li ke a buoy, and in actuali ty it might move in a circular motion, but it would NOT move with the wave.

V 8.5 Proposed method is descriptive, but shows a conceptual error. • Period: Confuses period and frequency. “ time how long it takes to go

from one peak to the next peak to find frequency.” E 7 Proposed method is too ambiguous to be carried out.

• Period: “use my stop watch to measure one complete cycle” but this instruction doesn’t make it clear when to start/stop timing.

• Wavelength: “you could use the meter stick to measure the distance of a wave which would give you wavelength” but this instruction doesn’t make it clear how to determine the distance.

S 6 Does not propose a method that can be carried out. • “measure peak to peak from the graph” but this doesn’t work because

you can’t generate a graph without already knowing the period/wavelength.

• “Determine the wavelength by measuring with the meter stick and the frequency by how many cycles it takes per second.”

P 5.2 Like S, but with an error. For instance, indicates that wavelength can be found from a y vs. t graph.

Z 5 Does not propose the method of finding period and wavelength to calculate wave speed.

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Quiz requirement b: method that works for a wave pulse

C: They are equally good

B

A

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Quiz requirement b: method that works for a wave pulse

C: They are equally good

B

A

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W 10 Gives clear instructions that could be carried out. • One example: hold the meter stick in place, oriented in the direction the

wave moves. Keep track of one wave crest as it travels down the stick. Begin time when the crest hits the fi rst end of the stick and stop time when the crest hits reaches the end. The wave has then traveled one meter in the time recorded on the stop watch. The speed in m/s is then (1 m/)(stopwatch time in seconds).

A 9.2 Proposed method is descriptive, but with a problem. • Like in W, but instead of watching a wave crest travel down the stick

plans to “ let go of the string” and time the string’s journey from one end of the stick to the other. As with “A ” above, the string would oscill ate in place, not travel with the wave.

T 7.7 Proposes measuring distance traveled in a time interval, but with a serious error: • Often considers the vertical distanced traveled (the ampli tude) to find the

speed at which the water’s surface moves up and down. This is not the same as the wave speed, which is the speed at which the wave propagates.

E 7 Proposed method is too ambiguous to be carried out. • Has idea of “see how many meters the water travels per some time” but

cannot progress further. R 5 Does not propose the method of finding how far the disturbance travels in a

given time interval. Often will write the wave equation and say something about finding the values in the equation, but this method will not result in wave speed. OR will propose alternative ways to get period and wavelength, but this wil l not fi t requirement (b) that one method work for a wave pulse.

X 3 Only proposes 1 method; other method blank C 0 Proposes no methods; both methods blank

Q 10 Identifies that wave is 2D R 0 States 1D S 0 States 3D T 0 Other/Blank

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Interference: When Waves Meet Phenomena:

Interfering pulses on the wave machine Interfering block-wave

Using Total Phase Equivalent total phase: Constructive Total phase separated by half-cycle:

Destructive

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Superposition of Waves The period and wavelength are exactly the same. One wave travels to the right, one to the left.

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Interfering Sound Waves

Greater pressure fluctuations

More & less intense means louder and softer

Greater amplitude

+

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Interfering Sound Waves

Amplitude is zero

+No more pressure fluctuations

No sound!

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Phase Chart for Interfering Waves Same rough format, but add difference

(most important part!)

2π 2π Unit circle

Wave 1

Wave 2

Difference€

t

T

€

x

λ

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What is responsible for the destructive interference in this case?

a) x=0b) x=/2c) xd) e) None of the above

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Introducing 2D Interference:The Ripple Tank Try to spot…

Places that are very deep Places that are very shallow Places that are “normal” depth Places two crest combine Places two troughs combine Places a crest meets a trough

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d

Two slits create two overlapping wave fronts

CrestTrough

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d

Two slits create two overlapping wave fronts

CrestTrough

What type of interference occurs at the marked spot?

a) Constructiveb) Destructivec) Partiald) Time-dependent

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d

Two slits create two overlapping wave fronts

CrestTrough

Why?

a) x=0b) x=/2c) xd) None of the above

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x2

Two slits create two overlapping wave fronts

CrestTrough

Why?

a) x=0b) x=/2c) xd) None of the above

x1

x1=x2 so x=0!

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d

Two slits create two overlapping wave fronts

CrestTrough

What type of interference occurs at the marked spot?

a) Constructiveb) Destructivec) Partiald) Time-dependent

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d

Two slits create two overlapping wave fronts

CrestTrough

Why?

a) x=0b) x=/2c) xd) None of the above

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d

Two slits create two overlapping wave fronts

CrestTrough

What type of interference occurs at the marked spot?

a) Constructiveb) Destructivec) Partiald) Time-dependent

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d

Two slits create two overlapping wave fronts

CrestTrough

Why?

a) x=0b) x=/2c) xd) None of the above

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d

Two slits create two overlapping wave fronts

CrestTrough

Why?

a) x=0b) x=/2c) xd) None of the above

x2x1

x1>x2 now…x1=2x2=1.5

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An interesting phenomenon: What are you seeing?

a) Constructive Interference Only

b) Destructive Interference Only

c) Pathlength-dependent Interference: both constructive & destructive depending on position

d) Pathlength-dependent interference: all types (const, dest, and partial) depending on position

e) Partial Interference

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Laser Interference

In DL you will use a shortcut to calculate pathlength difference: d sin = x