Simple Harmonic Motion Vibration / oscillation motion which Regularly Repeats itself Back and forth...

Simple Harmonic Motion

Vibration / oscillation motion which Regularly Repeats itself Back and forth

Cycle= complete to-and-fro motion Cycle=from peak to trough back to peak or From trough to peak back to trough

Period- the time it takes for one complete

cycle Frequency- The number of cycles completed

per second Frequency-measured in Hertz- cycles per sec. Frequency Units- 1/s or s-1

f=1/T T=1/f

0 ms 3.1 ms 6.3ms 9.6ms

Frequency = cycles per second

0 ms 3.1 ms 6.3ms 9.6ms

Frequency = cycles per second = 3 cycles /

0 ms 3.1 ms 6.3ms 9.6ms

Frequency = cycles per second = 3 cycles / 9.6 ms = 3 cycles /(.0096s) =

0 ms 3.1 ms 6.3ms 9.6ms

Frequency = cycles per second = 3 cycles / 9.6 ms = 3 cycles /(.0096s) = 312.5 Hz

0 ms 3.1 ms 6.3ms 9.6ms

Period = 1 / f

0 ms 3.1 ms 6.3ms 9.6ms

Period = 1 / f = 1 / 312.5 s = .0032 s or 3.2 ms on average

0 ms 3.1 ms 6.3ms 9.6ms

Period = 1 / f = 1 / 312.5 s = .0032 s or 3.2 ms on average

Period of oscillation of a Spring Mass System

Period of oscillation of Pendulum Mass System

Spring T=2 m k Dependent on mass and inversely related to the

spring constant Pendulum T=2 l g Dependent on length and inversely related to the

acceleration due to gravity

Natural Frequency – Forced Vibration-Resonance The frequency that a system occurs when a

force is applied to it. A Driving Force is a force that is applied over

and over again.

Natural Frequency – Forced Vibration-Resonance The frequency that a system acquires when

a force is applied to it. A Driving Force is a force that is applied over

and over again.

and over again. Resonance occurs when the driving force is

applied at the natural frequency or multiples of the natural frequency

Resonance produces large amplitude standing waves

Natural Frequency – Forced Vibration-Resonance Resonance caused the Tacoma Narrows

Bridge to collapse Resonance can cause a wine glass to break Resonance can is used in string instruments,

open end wind instruments, and closed end tube wind instruments

Standing Waves

Nodes points of destructive interference Antinodes points of constructive interference Standing waves are produced at natural

frequencies or resonant frequencies.

Standing Waves strings

L= n / 2 L = the length of a string Lambda equals the wavelength n = an interger n = 1 fundamental frequency n= 2 second harmonic n = 3 third hamonic

Standing Waves Open Springs continued.

Nodes are found at the fixed ends. Antinodes are not possible at the fixed ends

The velocity on a string is directly related to its tension and inversely related to the mass per unit length.

Standing waves open end tubes

Antinodes are possible at the open ends L=n / 2 L=length of the tube lambda wavelength n = 1 fundamental frequency n = 2 2nd harmonic n = 3 3rd harmonic

v= speed of sound v = (331 + .6 T) m / s

Standing waves closed end tubes

L = / 4 L = length of the tube lamda = wavelength antinodes are possible at the open end. nodes are possible at the closed end. Only odd harmonics are possible.

L = lambda / 4 L = length of the tube lamda = wavelength antinodes are possible at the open end. nodes are possible at the closed end. Only odd harmonics are possible.

The rising and falling of sound intensity is known as beats

The beat frequency tells you how many cycles per second the source frequency is different than the standard frequency.

The beat frequency does not tell you if the source frequency is higher or lower than the standard.

Doppler Effect

f=fo ( v + - vo )

( v - + vs)

vo = velocity of the observer

vs = velocity of the source.

vo =+ observer towards source f increases WHY?

vo = - source towards observer-f increases WHY?

Doppler Effect

f=fo ( v + - vo )

( v - + vs)

vo =+ observer towards source f increases WHY?

Multiply be a larger Numerator = Higher f

vo = - source towards observer-f increases WHY?

Divide by a smaller Denominator = Higher f

Wave Motion

Matter is not carried in mechanical waves. Energy is carried by mechanical waves. A wave has a velocity equal to the product

of.. its frequency and wavelength. V= f lamda

Wave Motion

of.. its frequency and wavelength. V= f

Wave Properties

Amplitude=maximum height relative to… The equilibrium Wavelength=distance between crests Frequency = the number of crests which pass

a given pt per second = cycle per sec = 1 Hz

Wave Properties

a given point per second = cycle per sec = 1 Hz

Wave Properties

Velocity of a Wave on a string

(m/l) FT= is the equal to the… Tension in the string. m / L is the … The mass per unit length of the string.

FT =Tension in the string. m / L is the … The mass per unit length of the string.

FT =Tension in the string. m / L is the … The mass per unit length of the string or..

FT =Tension in the string. m / L is the … The mass per unit length of the string or.. Linear Density in kg/m

Types of waves

transverse.. Oscillation is perpendicular to the wave

motion

(Electromagnetic waves are transverse waves

Types of waves

Longitudinal Oscillation is parallel to the wave motion (sound waves are longitudinal waves )

Types of waves

Longitudinal Oscillation is parallel to the wave motion (sound waves are longitudinal waves )

Speed of waves

The speed of a wave is directly related to the..

Elastic force factor and…. The interia factor (density of the medium

Speed of waves

The speed of a wave is directly related to the..

Elastic force factor and…. The interia factor (density of the medium

Wave intensity

Intensity is… The power transported across a unit area

perpendicular the energy flow of a wave. Intensity = energy / time divided by area Intensity = power / area Intensity = Watt / meters squared. The intensity of a wave decreases by 1/r2

Wave intensity

Decibels Relative measure of the perceived loudness of a

sound wave Decibels are based on a logarithmic scale dB=10 log ( Intensity of the sound wave ) ( Threshold of Human Hearing Intensity ) Threshold of Hearing = 1x10-12 W/m2

What is the intensity of a 75 dB sound wave? 75dB= 10 log ( I / Io) 7.5 = log ( I / Io) 7.5 = log I – log Io 7.5 = log I – log (1 x10-12 W/m2) 7.5 = log I – (-12) 7.5 – 12 = log I -4.5 = log I 3.16 x10-5 W / m2 = I

Decibels Relative measure of the perceived loudness

of a sound wave Decibels are based on a logarithmic scale dB=10 log ( Intensity of the sound wave ) ( Threshold of Human Hearing Intensity ) Threshold of Hearing = 1x10-12 W/m2

How many times more intense is a 120 dB sound wave

compared to a 80 dB sound wave? 120dB – 80 dB = 40 db 40 dB / 10 = 4 104 = 10,000 times greater

Wave Reflection-Fixed end

A single wave crest which reflects off a fixed end will leave as a single wave trough.

The wave crests puts a force up on the fixed end.

The fixed puts an equal but opposite force on the string which produces an equal but opposite wave trough.

Wave Reflection-Fixed end

A single wave crest which reflects off a fixed end will leave as a single wave trough.

The wave crests puts a force up on the fixed end.

The fixed puts an equal but opposite force on the string which produces an equal but opposite wave trough.

Wave Reflection-Free end

A single wave peak which reflects off a free end will leave as a single wave peak.

Simple Harmonic Motion Vibration / oscillation motion which Regularly Repeats itself Back and forth...

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