Transcript low pressure low pressure

It was a trick question – force is measured in Newtons, not kg.
Reminder: HW 7 is due Saturday at noon.
Reading for Tuesday: will be posted. Quiz Tuesday.
Questions to be answered today.
•How does a violin (or other stringed instrument) produce sound?
•Why do the different strings produce different notes?
•How does tuning and fingering and different types of bowing
change the sounds being produced?
All musical instruments have something that oscillates back and forth in periodic
fashion. (because a tone is air pressure oscillating back and forth)
Consider the violin. Each piece of string is like little mass hooked to spring.
First think about springs a little bit
Start a mass bouncing on a spring ...
Time of one oscillation
(Period)
Position
Relaxed
Spring
time
Positive
direction
Mass
Position
monitor
If the spring is stiffer, then …
a. the time per oscillation will increase
b. the time per oscillation will decrease
c. the time per oscillation will remain unchanged
Position
Time of one oscillation
(Period)
time
Mass
Fnet
Mass
Fnet
If the spring is stiffer, then …
a. the time per oscillation will increase
b. the time per oscillation will decrease
c. the time per oscillation will remain unchanged
When masses are at rest, forces exert upwards by springs are
equal. But if mass is displaced from rest position, stiffer spring
exerts greater force (=kx) upwards 
greater acceleration  faster turn around time shorter period 
higher frequency
Start a mass bouncing on a spring ...
Time of one oscillation
(Period)
Position
Relaxed
Spring
time
Positive
direction
Mass
Position
monitor
If the mass is heavier then …
a. the time per oscillation will increase
b. the time per oscillation will decrease
c. the time per oscillation will remain unchanged
Start a mass bouncing on a spring ...
Position
Time of one oscillation
(Period)
time
Mass
Mass
Fnet
Fnet
If the mass is heavier then …
a. the time per oscillation will increase
b. the time per oscillation will decrease
c. the time per oscillation will remain unchanged
If the 2 masses are displaced same amount from rest position, net
force up due to increase in spring force will exert be equal  gives
smaller acceleration for heavier mass
 slower turn around time  longer period  lower frequency
Start a mass bouncing on a spring ...
Time of one oscillation
(Period)
Position
Relaxed
Spring
Positive
direction
Mass
A
B
C
time
At which time is the kinetic energy of the mass
greatest?
Answer is B … KE = ½ mv2 … highest velocity!
Where does energy go at times A and C?
Position
monitor
Into the spring or gravitational potential energy
… Spring energy = ½ kx2
Tuning fork -- just like mass on spring, going up and down at
certain frequency.
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high pressure
(atoms close)
sound waves
traveling out
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to computer
hit microphone,
it flexes, makes voltage
V
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How violin makes sound- strings oscillate up and down.
Make body oscillate in and out, pushes air to make sound waves
sound waves
traveling out
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high pressure
(atoms close)
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to computer
hit microphone,
it flexes, makes voltage
V
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Look at the microphone signal from the big tuning fork.
If you do the same for the small tuning fork , what does the signal look like?
a. higher frequency b. lower frequency c. same frequency
Answer is a. Higher frequency, because there’s a smaller mass oscillating back
and forth at faster rate. Just like the spring when have a smaller mass vs a
larger mass.
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sound waves
traveling out
high pressure
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to computer
hit microphone,
it flexes, makes voltage
V
high pressure
Now pluck thickest violin string hard near the end of the string.
What will we hear and see with microphone?
a. Single freq./tone b. Two tones/freqs c. Many tones
c. Many tones.
sound waves
traveling out
low pressure
high pressure
(atoms close)
low pressure
to computer
hit microphone,
it flexes, makes voltage
V
high pressure
Now pluck thickest violin string soft in the center.
What will we hear and see with microphone?
a. Same mix of tones b. Different mix of tones.
sound waves
traveling out
low pressure
high pressure
(atoms close)
low pressure
to computer
hit microphone,
it flexes, makes voltage
V
high pressure
String oscillates back and forth. It’s tied down at each end.
The simplest way for the string to flex is like this:
But there are also higher harmonics …
Fundamental frequency, 1st harmonic
2nd harmonic, twice the frequency,
G3 string (in tune) gives the fundamental frequency 196 Hz
The 2nd harmonic harmonic on this string has frequency = 2 x 196 = 392 Hz
Notice how 2nd harmonic is same as the first harmonic of a string half as long.
If string ½ as long, then fundamental frequency would double.
A string is clamped at both ends and then plucked so that it vibrates in the
mode shown below, between two extreme positions A and C. Which
harmonic mode is this?
a. fundamental, b. second harmonic, c. third harmonic, d. 6th harmonic
A
These are snapshots at
different times.
B
C
answer: 6th harmonic- there are 6 places where the string is vibrating up and down
When the string is in position B, instantaneously flat, the
velocity of points along the string is...
A: zero everywhere.
B: positive everywhere.
C: negative everywhere.
D: depends on the position.
Answer : D. depends on position.
node: never moves.
A string is clamped at both ends and then plucked so that it vibrates in a
standing mode between two extreme positions A and C. Let upward motion
correspond to positive velocities.
A
1 2 3
B
snapshots at
different times.
C
When the string is in position B, instantaneously flat, the velocity of points
along the string depends on position.
When the string is in position C, the velocity of points along the string is...
A: zero everywhere.
C: negative everywhere.
B: positive everywhere.
D: depends on the position.
A: Zero Everywhere, all points along the string are turning around.
What is making the sound you hear?
a. string, b. the wood, c. both about the same, d. the bridge
b. The wood. String makes wood vibrate, which moves air to make the sound. The
wood can push a lot more air.
What will happen if we touch tuning fork to the bridge?
a. no effect, b. sound will be muffled (quieter), c. sound will be louder,
d. Sound will change frequency/tone
c. louder, because now the big wood panel is vibrating- more moving air,
louder sound.
Pluck string, measure microphone signal.
What will we see if we tighten string and do the same thing?
a. same, b. faster oscillations, c. slower oscillations.
Higher the tension means stiffer spring action …
b. tighter string pulls back harder, like stiffer spring
makes faster oscillations = higher frequency = higher tone.
Why is the pitch of the thinner string higher?
a. There’s more tension in the thinner string,
b. There’s less tension in the thinner string
c. The thinner string has less mass
d. The thinner string is longer
c. The thinner string has similar tension, but larger acceleration
because its mass is smaller
(Recall: the spring with the lighter mass went faster.)
Suppose we put down a finger to shorten the vibrating part of the
string. What happens to the pitch produced?
a. it’s the same,
b. it’s higher
c. it’s lower
b. faster oscillations = higher frequency.