finding mass of an astronaut in space
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Finding Mass of an Astronaut in Space
k
mT 2
This device consists of a spring-mounted chair in which the astronaut sits. The chair is then started oscillating in simple harmonic motion. The period of the motion is measured electronically and is automatically converted into a value of the astronaut’s mass, after the mass of the chair is taken into account. The spring used in one such device has a spring constant of 606 N/m, and the mass of the chair is 12.0 kg. The measured oscillation period is 2.41 s. Find the mass of the astronaut. (students work this.)
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Mass of an Astronaut
mN
kgms
/606
0.12241.2
k
mT 2
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Example 1 The Wavelengths of Radio Waves
AM and FM radio waves are transverse waves consisting of electric and magnetic field disturbances traveling at a speed of 3.00x108m/s. (What is this number?) A station broadcasts AM radio waves whose frequency is 1230x103Hz and an FM radio wave whose frequency is 91.9x106Hz. Find the distance between adjacent crests in each wave.
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16.2 Periodic Waves
Example 1 The Wavelengths of Radio Waves
AM and FM radio waves are transverse waves consisting of electric andmagnetic field disturbances traveling at a speed of 3.00x108m/s. A stationbroadcasts AM radio waves whose frequency is 1230x103Hz and an FM radio wave whose frequency is 91.9x106Hz. Find the distance between adjacent crests in each wave.
f
Tv
f
v
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16.2 Periodic Waves
AM m 244Hz101230
sm1000.33
8
f
v
FM m 26.3Hz1091.9
sm1000.36
8
f
v
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Problem
• Light travels at 3 * 10 8 m/s. Sound travels at 331 m/s.
• If lightning strikes 8.2km away from you, how long passes before you see it?
• How long passes until you hear it?
• (students work this.)
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Problem
• Light travels at 3 * 10 8 m/s. Sound travels at 331 m/s.
• V = d/t => t = d/v• If lightning strikes 8.2km away from you, how
long passes before you see it?• t = d/v = 8200m / 3 * 10 8 m/s• How long passes until you hear it?• t = d/v = 8200m / 331 m/s
• (students work this.)
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Problem
• So you see lightning hit 1 mile away, how many seconds do you count before you hear it?
• (students work this.)
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Problem
• So you see lightning hit 1 mile away, how many seconds do you count before you hear it?
• t = d/v = 1609m / 331 m/s
• So each 5 sec is about 1 mile away.
• Each 1 sec is about 3 football fields away.
• (Talk about military timing of artillery and nukes.)
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THE PRINCIPLE OF LINEAR SUPERPOSITION
When two or more waves are present simultaneously at the same place,the resultant disturbance is the sum of the disturbances from the individualwaves.
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Constructive Interference
• Two waves, a and b, have the same frequency and amplitude– Are in phase
• The combined wave, c, has the same frequency and a greater amplitude
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Destructive Interference
• Two waves, a and b, have the same amplitude and frequency
• They are half a cycle out of phase
• When they combine, the waveforms cancel
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Reflection of Waves – Fixed End
• Whenever a traveling wave reaches a boundary, some or all of the wave is reflected
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Reflection of Waves – Fixed End
• Whenever a traveling wave reaches a boundary, some or all of the wave is reflected
• When it is reflected from a fixed end, the wave is inverted
• The shape remains the same
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What happens when a wave interferes with its own
reflection?• Sometimes we get standing waves.
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1st Harmonic
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2nd Harmonic
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3rd Harmonic
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• The a string will only allow certain wavelengths to be standing waves.
• Because the endpoints need to be nodes.
• For a string with two fixed ends, – λ= 2L / n n = 1, 2, 3, 4 …….