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