chapter 5 let us entertain you
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Chapter 5 Let Us Entertain You. Sound and Light. How do stringed instruments make notes?. How do stringed instruments make notes?. Guitar. Ukelele. How do stringed instruments make notes?. Koto. Violin. How do stringed instruments make notes?. Piano. Harp. A word about pitch:. - PowerPoint PPT PresentationTRANSCRIPT
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