waves physics h. pendulum a pendulum is simply a mass (bob) suspended from a string that can swing...
TRANSCRIPT
Waves
Physics H
Pendulum• A pendulum is simply a mass (bob) suspended
from a string that can swing back and forth
• The time it takes for the pendulum to swing back and forth is called the period.
• Period depends on length of the pendulum, not on weight suspended.
• The back and forth motion is called simple harmonic motion (SHM)• Produces a sine curve
• The restoring force of a pendulum is a component of the bob’s weight• x-component pushes the bob toward equilibrium
• At small angles, a pendulum follows SHM• At large angles this breaks down
• Potential energy increases as displacement increases• Cons of energy still applies PE + KE = const.
Hooke’s Law• The following holds true
for a pendulum or a spring
• At the equilibrium point, v is a max
• At max displacement, force and “a” are max
• In SHM restoring force is proportional to displacement
• Hooke’s Law
• Felastic = -kx• k = spring constant
• x = displacement
• - = force is always opposite direction from displacement
• See Figure 12-1
• A stretched or compressed spring has elastic potential energy
Sample Problem 12A
• If a mass of .55kg attached to a vertical spring stretches the spring 2.0cm from it’s equilibrium position, what is the spring constant?
• Not accelerating so Nnet = 0
• Fnet = 0 = Felastic - FW
• -kx – mg = 0
• Rearange k = -(mg)/x
• k = -(.55kg)(9.8m/s2)/(-.02m)
• k = 270 N/m
Pendulum Mass-Spring
The period of a simple pendulum can be calculated with
period = 2Π x square root of length / gravity
• Period of a mass spring system in SHM
• period = 2Π x square root of mass / spring constant
g
LT 2 k
mT 2
Ex
• When a mass of 25g is attached to a certain spring, it makes 20 complete vibrations in 4.0s. What is the spring constant?
• Calculate period first• 4.0s/20vibrations = .2s / vibration
• Now use the formula
k
mT 2
• .2s = 2Π√(.025kg/k)
• .1s/ Π = √(.025kg/k) square both sides
• .00101s2 = .025kg / k
• k = 25 N/m
Sample Problem 12B
• You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and that its period is 12 s. How tall is the tower?
Sample Problem 12C
• The body of a 1275 kg car is supported on a frame by four springs. Two people riding in the car have a combined mass of 153 kg. When driven over a pothole in the road, the frame vibrates with a period of 0.840 s. For the first few seconds, the vibration approximates SHM. Find the spring constant of a single spring.
• Homework
• 12A-C odd
Wave Motion
• Mechanical waves travel by molecules vibrating back and forth or up and down. • Sound, ocean wave
• They have to travel through a medium• Water, air
• Pulse – single traveling wave
Wave Types
• Transverse Wave - Motion of the wave is at right angles to the direction the wave is moving.
• Longitudinal Wave - Motion of the wave is in the same direction as the direction the wave is moving.
Wave Description
• Waves are made up of several parts
• Crests - high points
• Troughs - low points
• Amplitude - distance from the midpoint to the crest or trough
• Wavelength - distance form the top of one crest to the top of the next.
• Frequency - How often a vibration occurs.
• Period - amount of time for 1 cycle
Wave
Frequency
• Frequency measures the number of times a wave oscillates in a given time (second)
• Frequency is measured in hertz• 1 cycle per second = 1 hertz
• frequency = 1/period
• period = 1/frequency
Wave Speed
• Wave speed depends on what type of medium it is traveling through
• The speed of a wave is dependant upon 2 things, wavelength and frequency
• Wave speed = wavelength x frequency
• v = f
Examples
• The Sears tower swings back and forth at a frequency of .1Hz what is its period?
• What is the wavelength of a 170Hz sound wave when the speed of sound in air is 340m/s?
• Frequency = 1/period
• .1Hz = 1/period
• Period = 10s
• v = f• 340m/s =(170Hz) = 2.0m
Sample Problem 12D
• The piano string tuned to middle C vibrates with a frequency of 264 Hz. Assuming the speed of sound in air is 343 m/s, find the wavelength of the sound waves produced by the string.
Interference
• Occurs every time two waves overlap• Constructive - When crests of two waves
overlap, it results in increased amplitude. The waves are said to be in phase
• Destructive - When the crest of one wave overlaps with the trough of another wave, they cancel each other out. The waves are said to be out of phase with each other.
• .
Reflection
• When ever a wave transfers from one medium to another, part of the wave reflects and part of the waves energy continues on.
• At a free boundary, waves are reflected.
• At a fixed boundary, waves are reflected and inverted.
Standing Waves
• If a string attached to a wall vibrates at exactly the right frequency, it can produce a standing wave.
• Standing Wave- A wave pattern that does not move along the string.
• Node – There is no motion on the string• Antinode – midway between the nodes,
vibrations have the largest amplitude
Review
• What are the two types of interference?
• How fast is a wave with a wavelength of 3m and a frequency of 212Hz moving?
• Describe the two types of waves.
• If a wave has a period of .2s, what is its frequency?
• A radio station has a frequency of 101 MHz, what is the period of its wave?
• What are the two points of importance on a standing wave?
Chapter 12 Review
• p. 469 #8-9
• p. 470 #19-22 and 35
• p. 471 #36