Today: Energy, Standing Waves, Resonance, Sound Waves

Exam questions will be similar to quiz questionsEssential that you practice the quizzes!

Covering material including this weekQuiz #3 Tuesday before class (covered on exam).Exercises will be due before class Tuesday.

Exam #1 is one week from ThursdayIn this room, BRING A PENCIL!!!

http://www.physicscurriculum.com/Photos/Sound1.JPG

Homework problem…conservation of energy

#1 #2

20 mphInitial speedfor both

Same initial height

Q: Which hits ground with more speed? (neglecting air resistance)

First, let’s discuss in groups!

A.Ball #1B.Ball #2C.Both are the same

Some good student answers“Some!”—many good ones not here, sorry

Lisa: "The way I understand conservation of energy is that it can not be created or destroyed, it can be transformed into one form or another, but the amount of energy does not change. So, I would say that both balls have the same amount of speed when they hit the ground regardless of being thrown upward or downward because the amount of energy does not change regardless of the directions the balls are thrown. "

Ritchy : "... and will hit the ground at the same velocity. Of course if the second ball is made from enriched uranium.... "

Ritchy : "... and will hit the ground at the same velocity. Of course if the second ball is made from enriched uranium.... "

John : "...After passing this point, ball # 2 will fall with the same speed as # 1 did and will follow the same trajectory, and therefore will hit the ground with the same speed ball # 1 did. "

Adrian: “…it would regain the speed it had traveling upwards because it would not have transfered that energy elsewhere."

Brian : "The law of the Conservation of Energy states that energy can be transformed but never created or destroyed. Because both balls are being thrown at the same speed in the same gravitational zone both balls have the same amount of energy and therefore will hit the ground at the same speed...

Reuben: So while they will hit the ground at different times they will be at the same speed when they hit. "

Audrey : "..The same amount of energy put in will be the same till it hits the ground because nothing is getting in its way. This is a trick question. "

Aubrey: "Think of how ball #2 would look on a graph. It's velocity would slightly decrease until it reached the top of its path, and then increase on its way down until it hit the ground. Its velocity would be mirrored, then, the same on the way up as the way down...."

Aubrey: "Think of how ball #2 would look on a graph. It's velocity would slightly decrease until it reached the top of its path, and then increase on its way down until it hit the ground. Its velocity would be mirrored, then, the same on the way up as the way down...."

Homework problem…conservation of energy

#1 #2

20 mphInitial speedfor both

Same initial height

Q: Which hits ground with more speed? (neglecting air resistance)

You could analyze with F = ma,Equations of motion, etc.

But much easier using conservation of energy!

Homework problem…one viewpoint

#1 #2

20 mphInitial speedfor both

Same initial height

Q: Which hits ground with more speed? (neglecting air resistance)

Which one has higher initial total energy (KE + PE)?

Can the ball lose total energy while inthe air (without air resistance)?

KE = ½ m v2

PE = m g h

So which one would have more energy when hitting ground?

Homework problem…another viewpoint

#1 #2

20 mphInitial speedfor both

Q: Which hits ground with more speed? (neglecting air resistance)

If energy is conserved, then whatwill be the speed of ball #2 when itreturns to the point it started?

#2

? mph

Potential energy is the same…

Given that information, which ballwould hit faster?

Check student answers on WebCT (tomorrow night?)Answer is: same speed

Think about energy flow and conservation of energy…thisplays a part in waves too.

Clicker question--wavelength

Let’s discuss this one in groups

Frequency and speed are the fundamental properties of a wave

The frequency of the wave is determined by the frequency of the driving oscillation.(and possibly motion of the source…Doppler)

The speed of the wave is determined by the physics of the material.

The wavelength (e.g. distance between crests) is determined by the frequency and speed.

Wavelength =Wave speed

frequency

(Wave speed = wavelength x frequency)

Reminder about amplitude and wavelength

Standing waves are the result of interference

Interference of waves is addition of wavesWaves have “+” and “-” regions for addingWave interference is a really important physics

concept

Today, we’ll look at interference as the cause for standing waves.

What will happen when these waves meet?

Falstad ripple tank applet

Standing waves are the result of interference

Interference of waves is addition of wavesWaves have “+” and “-” regions for adding

Standing waves result from interference of a wave with its own reflection…only for special conditions http://www.falstad.com/ripple/

I wish we could look at wave interference with a real demo!

Wave table!Wave table!

Standing waves…stored energy

Energy is “stored” in the wave…no net transportBut results from the movement of energy BOTH ways!

Antinode,Highest energy

Node,Lowest Energy

Energy flow?

Standing wave youtube demo http://www.youtube.com/watch?v=yCZ1zFPvrIc

Clicker Question—Standing Waves

The picture to the right is a schematic of a standing wave on a stretched rope.

Which point labels an antinode?

A B

Clicker Question—Standing Waves

The picture to the right is a schematic of a standing wave on a stretched rope.

Which point labels an antinode?

“A” is an antinode…antinodes are places with the highest amplitude…and the highest energy (“B” is a “node”)

A B

Standing waves…only some “modes” will work

Modes must satisfy “boundary conditions”In this case, the ends must be antinodes for

constructive interference.

Notice thespecial frequencies

Can only controlthe frequency,not wavelength!

These special frequencies are

resonant frequencies of the

wave table(missing the citation forthis wavetable video)

Resonance

Resonance occurs when an wave is driven at the correct frequency for a standing wave

Disastrous resonance demos

Resonance a key to musical tones (more later)This gets us to sound waves

The classic: http://www.youtube.com/watch?v=17tqXgvCN0E&feature=related|Also Tacoma

MIT Resonance Demo http://www.youtube.com/watch?v=aZNnwQ8HJHU

Clicker Question—Sound waves

If we could see a pure tone sound wave in the air, which of the following would we see?

A) Transverse displacements of molecules as in a wave on a string

B) Alternating regions of high density and low density

C) Twisting motion of air as in the wave table

Clicker Question—Sound waves

If we could see a pure tone sound wave in the air, which of the following would we see?

A) Transverse displacements of molecules as in a wave on a string

B) Alternating regions of high density and low density

C) Twisting motion of air as in the wave table

Sound waves are longitudinalcompression / rarefaction waves

Reminder of difference betweentransverse and longitudinal waves

Transverse Wave

Longitudinal wave

Imagine this is a speaker

(sorry, I am missing the citations for these animated gifs)

Sound in air is aCompression / Rarefaction Wave

Slinky

Flame tube

I’ll describe what the flame tube is. How should a standing wave of pressure nodes / antinodes affect the flame?

Note: we ran out of time here and did not get to discuss the following slides in today’s lecture (Feb. 3,

2009)

Last week’s puzzler:Wind and Doppler Effect

Does the wind affect the pitch of a factory whistle you hear on a windy day?

1. Yes2. No

Another perspective, may cause “aha!”:

What if both the whistle and the person were moving in the same direction? Is that any different than a wind blowing?

The compression / rarefaction waves are

what you hear…

Remember it’s the frequency that

determines the pitch

Last week’s puzzler:Wind and Doppler Effect

Does the wind affect the pitch of a factory whistle you hear on a windy day?

1. Yes2. No

Another perspective, may cause “aha!”:

What if both the whistle and the person were moving in the same direction? Is that any different than a wind blowing?....CLICKER Q!

1. Yes

2. No

Does the wind affect the pitch of a factory whistle you hear on a

windy day?

Author’s very good analogy, why wind does not affect pitch of sound

If the first guy is only putting down items once per second…

How could a faster belt increase the number of items per second the second guy can pick up?

Ripple tank applet for Doppler Effecthttp://www.falstad.com/mathphysics.html ripple

Nerf Doppler Demo

Possibly this applet if it works http://physics-animations.com/Physics/English/waves.htm