Chapter 5Let Us Entertain You.

Sound and Light

How do stringed instruments make notes?

How do stringed instruments make notes?

Guitar

Ukelele

KotoViolin

How do stringed instruments make notes?

PianoHarp

How do stringed instruments make notes?

A word about pitch:

High note = High pitch = High frequency

Low note = Low pitch = Low frequency

A vibrating string:

• What affects the frequency of vibration?

Frequency is……

• ______________related to the ___________ of the tension on the string

• ______________related to the ___________ of the length of the string

• ______________related to the ___________ of the mass of the string

Frequency is……

• ____Directly___ related to the _square root_ of the tension on the string

• ___Inversely___ related to the _square root_ of the length of the string

• ___Inversely___ related to the _square root_ of the mass of the string

Frequency is….

f= T 4mL

Waves:

• Carry energy (Greater amplitudemore energy)

• Have a velocity, wavelength, frequency and amplitude (Frequency and wavelength are inversely related)

• Velocity depends on the medium• Interfere (add up)• Can be transverse (↕) or longitudinal (↔)

The wave equation:

Velocity = frequency x wavelength

v = f l(m/s) = (/s) x (m)

(frequency and wavelength are inversely related)

Calculate:1) Waves on water have a wavelength of 2.0 m,

and a frequency of 3 Hz (3 waves / second). What is their speed?

2) A vibrating guitar string has a frequency of 512 Hz, carrying a wave that moves at 320 m/s. What is its wavelength?

3) What is the frequency of a radio wave that travels at 3.00 x 10 8 m/s and has a wavelength of 3.134 m?

Wave motion

Wave motion

Motion of medium

Motion of medium

What is the wavelength in each

case

Woodwinds.

• The resonance of sound in an open tube:

• Please notice the antinodes at the open ends.

Woodwinds.

• What is the length of the entire wave?

Woodwinds.

• What is the length of the entire wave?

• The tube holds half a wave, so l=2L

Other resonance modes: What is the wavelength

in each case?

In a tube of air, the length of the tube is…

If one end is closed:

• There is a node at the closed end, and an antinode at the open end.

If one end is closed:

• There is a node at the closed end, and an antinode at the open end.

• What is the length of the wave?

If one end is closed:

• There is a node at the closed end, and an antinode at the open end.

• One-fourth of the wave fits into the tube, so l=4L.

Other resonance

modes: What is the wavelength

in each case?

HW p 526

• 1) (Pretty good)• Similar: vibrations make sound, frequency

and wavelengths• Different: String vibrating makes air vibrate vs

air itself vibrates

HW p 526

• 2) a. Did you draw them (3 or 4) full-sized?• b.

HW p 526

• 2) b. (cont’d)

• c) longest wavelenths=lowest frequencies

HW p 526

3) answers vary (2.4 m normally—19.5 m record)b.

c. L of pipe= ¼ wavelength• (wavelength=4 x L of pipe)

• d freq and wavelength are inversely related.

HW p 526

4) L of pipe= ¼ wavelength• (wavelength=4 x L of pipe)• f=v/l

5) Which is higher? How much higher freq.?f=v/l, freq and wavelength are inversely related.

6) t=d/v

Apply the wave equation:1. A wave has a frequency of 58 Hz and a speed of 31 m/s. What is

the wavelength of this wave? 2. A periodic transverse wave is established on a string such that

there are exactly two cycles on a 3.0-m section of the string. The crests move at 20 m/s. What is the frequency of the wave?

3. A 4-m long string, clamped at both ends, vibrates at 200 Hz. If the string resonates in six segments, what is the speed of transverse waves on the string?

4. Four standing wave segments, or loops, are observed on a string fixed at both ends as it vibrates at a frequency of 140 Hz. What is the fundamental frequency of the string?

5. Vibrations with frequency 600 Hz are established on a 1.33-m length of string that is clamped at both ends. The speed of waves on the string is 400 m/s. How many waves are on the string?

Light

• Light is a transverse wave (an electromagnetic wave)

• Light travels in a straight line

Light

• A shadow falls where light is blocked

Shadow

No shadow

No shadow

Light

• A shadow falls where light is blocked…BUT!

Shadow

No shadow

No shadow

Light

• A shadow falls where light is blocked…BUT…a real light source is not a single point.

Light

• A shadow falls where light is blocked…BUT…a real light source is not a single point.

Shadow from the right side of the bulb

Light

• A shadow falls where light is blocked…BUT…a real light source is not a single point.

Shadow from the left side of the bulb

Light

• A shadow falls where light is blocked…BUT…a real light source is not a single point.

Overlapping shadows (umbra)

Light

• A shadow falls where light is blocked…BUT…a real light source is not a single point.

Non-overlapping shadow (penumbra)

Non-overlapping shadow (penumbra)

Light

• A shadow falls where light is blocked…BUT…a real light source is not a single point.

Light from both sides (no shadow)

Light from both sides (no shadow)

Umbra and Penumbra

Umbra and

Penumbra

Tracing Rays.

dido

dido

di=doThe image is directly behind the mirror at the same distance the object is in front of

the mirror

dido

Tracing Rays II

Tracing Rays II

Tracing Rays II

Tracing Rays II

Measure angle of incidence

Measure angle of reflection

Angle of incidence=angle of reflection

Curved mirrors

• A convex mirror takes light rays parallel to the axis and makes reflected rays that diverge

Curved mirrors

• The reflected light seems to come from a single point behind the mirror, the focus

focus

Curved mirrors

• A concave mirror takes light rays parallel to the axis and makes reflected rays that converge

Curved mirrors

• The reflected light goes through a single point in front of the mirror, the focus

focus

So, where’s the image?

So, where’s the image?

• It depends.

Curved mirrors• In a convex mirror, an image is formed where

the rays seem to come from.

Curved mirrors• The image is upright, smaller, and can be seen

in the mirror.

Curved mirrors

• In a concave mirror, the image is inverted (upside down) and can be projected onto a screen

Curved mirrors

• Here, the image is smaller than the object.

Curved mirrors

• …but you can make a real image just as large…

Curved mirrors

• …or even larger than the object.

Did you notice?

As do gets smaller, di gets larger!

Did you also notice?

As do gets smaller, di gets larger!

As di gets larger, hi gets larger!

A concave mirror can also make a virtual image.

Draw three rays.

• 1) Parallel to the axis—reflects through the focus

Draw three rays.

• 1) Parallel to the axis—reflects through the focus

Draw three rays.

• 2) To the center—reflects like a flat mirror

Draw three rays.

• 2) To the center—reflects like a flat mirror

Draw three rays.

• 3) To the focus—reflects parallel to the axis

Draw three rays.

• 3) To the focus—reflects parallel to the axis

Draw three rays.

• All together:

Draw three rays.

• All together

Rules, rules, rules.

1) A real image has a positive di and hi. It is inverted (upside down = positive height!)

2) A virtual image has a negative di and hi. It is upright (right side up = negative height!)

3) A real image has a real location—put a screen there. A virtual image has a virtual location, it looks like it is there in the mirror.

Rules, rules, rules.4) A virtual image can be larger, the same size or smaller than the object

larger—in a concave mirror the same size—in a flat mirror smaller—in a convex mirror

5) A real image can be larger, the same size or smaller than the object

larger—if di is larger than do

the same size—if di is equal to do

smaller—if di is smaller than do

The lens equation.

(I know, we’re using mirrors, it’s the same equation)

1 = 1 + 1 f do di

The lens equation.

(I know, we’re using mirrors, it’s the same equation)

1 = 1 + 1 f do di

and di = hi

do ho

What do you notice?

What do you notice?

• If you pull the object in (decreasing do), the image moves away from the focus (increasing di)

• As the image moves away from the focus, it gets larger.

Describe the image formed:

1. A 12.0 cm object is placed 24.0 cm. from a concave mirror with a focal length of 18.0 cm.do=24.0cm

di=

f=18.0 cmho=12.0 cm

hi=

Describe the image formed:

1. A 12.0 cm object is placed 24.0 cm. from a concave mirror with a focal length of 18.0 cm.do=24.0cm

di=72.0 cm Real image!

f=18.0 cmho=12.0 cm

hi=36.0 cm Inverted and larger!

Describe the image formed:

2. A 8.0 cm object is placed 15.0 cm. from a concave mirror with a focal length of 6.0 cm.do=15.0 cm

di=

f=6.0 cmho=8.0 cm

hi=

Describe the image formed:

2. A 8.0 cm object is placed 15.0 cm. from a concave mirror with a focal length of 6.0 cm.do=15.0 cm

di=10.0 cm Real image!

f=6.0 cmho=8.0 cm

hi=5.33 cm Inverted and smaller!

Describe the image formed:

3. A 6.0 cm object is placed 4.0 cm. from a concave mirror with a focal length of 6.0 cm.do=4.0 cm

di=

f=6.0 cmho=6.0 cm

hi=

Describe the image formed:

3. A 6.0 cm object is placed 4.0 cm. from a concave mirror with a focal length of 6.0 cm.do=4.0 cm

di= -12.0 cm Virtual image!

f=6.0 cmho=6.0 cm

hi=-18.0 cm Upright and larger!

Describe the image formed:

4. A 12.0 cm object is placed 12.0 cm. from a convex mirror with a focal length of -18.0 cm.do=12.0 cm

di=

f=-18.0 cmho=12.0 cm

hi=

Describe the image formed:

4. A 12.0 cm object is placed 12.0 cm. from a convex mirror with a focal length of -18.0 cm.do=12.0 cm

di=-7.20 cm Virtual image!

f=-18.0 cmho=12.0 cm

hi=-7.20 cm Upright and smaller!

Refraction of light.

• Light bends when it enters or leaves a transparent object.

Refraction of light.

• Light bends when it enters or leaves a transparent object…because light travels more slowly in the substance.

Light slows down

Light speeds up

Which way does it bend? How far?

Which way does it bend? How far?

• Measure from the normal line

Angle of incidence

Angle of refraction

Snell’s Law

• The index of refraction for a substance, n, is defined: n= sin i

sin r

Angle of incidence

Angle of refraction

Snell’s Law

• Light bends towards the normal as it enters a substance from air.

Angle of incidence

Angle of refraction

Snell’s Law

• Light bends away from the normal as it leaves a substance to air.

Angle of incidence

Angle of refraction

Snell’s Law

• The index of refraction relates the sines of the angles.

Angle of incidence

Angle of refraction

Pop quiz:

For what angle, , is

Sin >1?

Pop quiz:

For what angle, , is

Sin >1?

None!

Snell’s Law

• Light leaves the substance when it can…

Angle of incidence

Angle of refraction

Snell’s Law

• Light leaves the substance when it can…but how far away from the normal can it bend?

Angle of incidence

Angle of refraction

Snell’s Law

?

Snell’s Law

Total internal

reflection!

Snell’s Law

Total internal

reflection!Critical angle!

When angle of refraction= 90o

Try this one:

Try this one:

Try this one:

Try this one:

Try this one:

Or:

Or:

Or:

Or:

A diamond has a large index of

refraction (=small critical angle)

Or:

It is cut so that all light reflects off

the bottom, escapes out of

the top