herriman high honors physics chapter 11 vibrations and waves

Herriman High Honors Physics

Chapter 11

Vibrations and Waves


Hooke’s Law

Remember that for springs, the spring constant, K = . The units are N/m.

This means that F = kx

Practice AP. 371Problems 2 & 4


Simple Harmonic Motion When a vibration or an oscillation

repeats itself back and forth over the same path, the motion is said to be periodic.

The most common oscillation come from springs and you will recall from earlier chapters that the description of a spring’s oscillation requires some vocabulary.


Oscillation of a Mass on a Spring

Top picture is “rest position”; x = 0

Bottom picture is “stretched position” Here x represents the

displacement. Maximum displacement is

called the amplitude. One cycle refers to one

complete to and fro motion. The period, T represents

the time for one cycle. The frequency, f is the

number of cycles in a given time period, usually one second.


Relationship between Frequency and Period

Frequency – the number of cycles in one second

Period – the time required to complete one cycle.

Hence the relationship between period and frequency is:

F = 1/T or T = 1/F Where period is measured in seconds and

frequency is measured in hertz (hz) which is 1/seconds.


Sample Problem

A spring stretches 0.150 m when a 0.300 kg mass is attached to it. The spring is then stretched an additional 0.1 m from its equilibrium point and released. Find A) the spring constant K B) The amplitude of the oscillation C) The maximum velocity


Solution K = F/x = (.3 kg)(9.8 m/s2)/.150 m = 19.6

N/m A = .1 m (can’t move further than where

originally released, conservation of energy)

½ mv2 = ½ Kx2 so

808.03.

6.191.

m

KAV


Period of any Oscillating Body From this equation we can derive an

equation for the period of any oscillating body

K

mT 2

Which for the special case of a pendulum becomes:

g

LT 2


Sample Problem

A pendulum is 2 meters long. What is its period on earth where gravity is 9.8 m/s2?

What would the period of the same pendulum be on the moon where gravity is 1.63 m/s2?


Solution

On Earth

83.28.9

222

g

LT

On the moon

95.663.1

222

g

LT

Practice BP. 379

Problems 2 & 4

Practice CP. 381

Problems 1,3, & 5


Waves Waves are a form of periodic motion. Two types of Waves

(classified by movement) Transverse

Wave moves perpendicular to amplitude Longitudinal

Wave moves parallel to the amplitudeClassified by medium

Mechanical Require a Medium

Electromagnetic Do not require a medium


Wave Vocabulary

For a Transverse Wave Top – Crest Bottom – trough Wavelength (λ) – distance from crest to

crest or trough to trough Frequency – number of waves or cycles

per second Velocity – speed of wave


Wave Vocabulary

For a Longitudinal Wave front – compression Back – rarefaction Wavelength (λ) – distance from

compression to compression or rarefaction to rarefaction

Frequency – number of waves or cycles per second

Velocity – speed of wave


The Wave Equation

By DefinitionV = fλ

Where v = wave velocity (meters/second) f = wave frequency (hertz) λ = wavelength in meters.


Sample Problem

A boy sitting on a beach notices that 10 waves come to shore in 2 minutes. He also notices that the waves seem to be about 20 meters apart as they travel on the ocean. What is the frequency of the waves? What is the velocity of the waves?


Solution

f = waves/second = 10/120 = 0.083 hertz

V =fλ =(0.083 hz)(20 meters) =1.66 m/s

Practice DP. 387

Problems 2 & 4

Interference

When two waves pass through each other they are said to form an interference pattern according to the superposition principle.

To use this principle you superimpose the waves - draw one on top of the other, and look at the resulting wave pattern.



Superposition Principle

There are two types of interference Constructive

interference Waves reinforce

each other (a) Destructive

interference Waves cancel each

other (b)


Reflection at a boundary

Reflection at a fixed boundary are inverted. (a)

Reflection at a free boundary comes back upright. (b)

Standing Waves When a wave and its reflection

reinforce in such a way that the result appears to be stationary, we call this a standing wave. In a standing wave the parts which

destructively interfere or cancel are nodes and the parts which constructively interfere or reinforce are called anti-nodes.



Standing Waves 1st harmonic

2 nodes (each end), 1 anti-node.

λ = 2L 2nd harmonic

3 nodes,2 anti-nodes. λ = L

3rd harmonic 4 nodes,3 anti-nodes.

herriman high honors physics chapter 11 vibrations and waves

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