Vibrations and Waves

Physics – 5th 6wks

• Vibration – a repeated back-and-forth motion, around a

fixed position. (a wiggle in time)

• Wave – a rhythmic disturbance that transfers energy

through matter or space.

• A wave is the physical effect of the movement of energy.

• A wave exists only as long as it has energy to carry.

• The source of all waves is something that vibrates (or

wiggles if you will)Mythbusters - Metal Fusion Shockwave – YouTube

Russian Meteorite Blast Wave Impact

Nuclear Blast Wave from 1950s era

High Speed of Massive Gunpowder Explosion

Waves & Vibration: Introduction

Mythbusters: Shockwave

Blast Waves

Period, Cycle, and Simple

Harmonic Motion

• Each complete vibration is known as a cycle.

• Period – the time required to complete one cycle.

• A reoccurring, back and forth motion (like that of a swinging pendulum) is called simple harmonic motion.

Simple harmonic

(or periodic)

motion

Transverse Waves

• Transverse Waves – waves in which the motion of the medium

(what the wave is traveling through) is at right angles to the

direction that the wave is moving.

• Waves on the surface of liquids, stretched musical strings, and

the different forms of light are transverse waves.

• A pendulum that is undergoing simple harmonic motion, would

trace out a transverse wave in its movement.

Transverse Wave

Parts of a Transverse Wave

• The high points on a wave (the peaks) are known as crests.

• The low points on a wave are called troughs.

• The midpoint of the vibration, often represented by a dashed

line, is called the point of equilibrium.

Point of equilibrium or

the midpoint

Parts of a Transverse Wave

• Amplitude is the distance from the midpoint, or point of equilibrium and

either the crest or trough of the wave.

• The amplitude then equals the maximum displacement from

equilibrium.

• The greater energy that a wave has, the greater its amplitude is.

• The wavelength of a wave is the distance from the top of one crest to

the top of the next one.

• The wavelength, to put simply, is the distance between two identical

parts of a wave.

Point of equilibrium or

the midpoint

• Sometimes the particles of the medium move back and forth in the

same direction in which the wave travels.

• Longitudinal Waves – waves in which the particles move along

the direction of the wave rather than at right angles to it.

• Also known as Compressional Waves or Mechanical Waves.

• Sound Waves are longitudinal waves.

• sound waves and a Rubens Tube

• Rubens Tube and basic tones

Longitudinal Waves

• The dense, compressed area of a longitudinal wave is

called a Compression.

• The lower density region of a longitudinal wave is called a

Rarefaction.

• The wavelength is measured either between two

compressions or two rarefactions.

• The more dense the medium becomes upon compression,

the greater the longitudinal wave’s amplitude.

Longitudinal Waves

Longitudinal Wave

Slink Drop

How does a Slinky fall?

Super-sized Slow-Mo Slinky

Super Slow-Mo Slinky

Slinky Drop Explained

Parts of a Longitudinal Wave

wavelengthrarefaction

compression

Ruben’s Tube & Sound Waves

Rarefaction Compression

A Rubens’ Tube is a metal tube sitting horizontally with tiny holes drilled in a line

along the top. One end of the Rubens’ Tube is connected to a small tank of propane like

those used when camping, and the other end of the Tube is connected to a speaker.

When a sound is played through the speaker, the wave of energy compresses the

propane gas inside of the tube and propane escapes out of the tiny holes on top. If the

gas coming out of the holes is ignited, the flames will be taller where the gas is

compressed and shorter where the gas particles are less dense.

Reuben’s Tube Basics

2-D Reuben’s Tube

Reuben’s Tube: Dubstep

Waves through Water

• Note waves of energy through water can behave like longitudinal

waves in the water and as transverse waves on the surface where the

water meets the air.

Earthquake/Seismic Waves

• Earthquakes move as a combination of the two – as

P waves (pressure waves – or longitudinal) and S Waves

(transverse waves). Matter tends to move in an elliptical pattern as

the waves of energy move through the ground

Frequency

• How often a vibration occurs is described by its frequency

• One back and forth motion would be a cycle.

• If this happened in one second, the frequency would be 1 cycle

per second. If two vibrations happened in 1 second, the

frequency would be 2 cycles per second, etc.

• The unit for frequency is called the Hertz (named after the

German scientist Heinrich Hertz who was the first to produce &

receive radio waves) and its symbol is Hz

• A frequency of 1 cycle per second is equal to 1 Hz and a

frequency of 2 cycles per second is equal to 2 Hz , and so on.

The relationship between Period and

Frequency

• If the frequency of a vibrating object is

known, its period can be calculated, and vice

versa.

• If something vibrates twice in 1 second, its

frequency is 2 Hz . Therefore, the time it

took for one vibration to occur was ½ second.

• If the frequency of an object was 3 Hz, then

the period or time for one vibration to occur

would be 1/3 sec .

• The period then is the reciprocal of the

frequency and the frequency is the

reciprocal of the period.

• Note: raising anything to the negative one

power is the same as finding its reciprocal

(or dividing it into 1)

Note: Frequency is in Hz

Period is in seconds

Circle diagram for the relationship between

Period & Frequency of a Wave or Vibration

1

T F

T = Period (of time)

F = Frequency

T=1

𝐹

F = 1

𝑇

Units:

Period = seconds

Frequency = Hz

1 = T × 𝐹

Remember: that 1

𝐹is the same as doing 𝐹−1

Example Problem 1: Period from Frequency

If something vibrated 30 times every second (meaning it had a frequency

of 30 Hz) how long did it take it to vibrate once?

Period = 1 𝑠𝑒𝑐

30

take the inverse of 30 Hz (or 30/sec)

Period = 1

30sec

Period ≈ 0.03 𝑠𝑒𝑐

Example Problem 2: Frequency from the Period

If something vibrated once every 0.25 sec, at what frequency did it

vibrate at?

Frequency = 1

0.25 𝑠𝑒𝑐

take the inverse of 0.25 sec

Frequency = 4 Hz that is, 4 times every second

Wave Speed

• Speed, frequency, and wavelength of a wave are related.

• In the formula for wave speed, speed is v, frequency is f, and

wavelength is the Greek letter Lambda - λ

• The units for wave speed are always a derived unit of distance divided

by time.

• If the wavelength between two crests of waves on the ocean is 3

meters, and 2 crests pass by a stationary point each second, then the

wave speed is 3 meters x 2 cycles/second = 6 meters/second.

Note: frequency will be in Hz, wave speed will be in m/s, and wavelength will be in m

Circle diagram for the Wave Speed formula

v

λ f

v = wave speed

λ = wavelength

f = frequency

λ=𝑣

𝑓

f = 𝑣

λ

Units:

Wave Speed = meters/second

Frequency = Hz

Wavelength = meters

v = λ × 𝑓

Example Problem #3: Finding Wave

Speed

The frequency of a wave is 40 Hz, and the wavelength of the wave is

0.8m. What is the speed of the wave?

𝑣 = 40 𝐻𝑧 × 0.8 𝑚

𝑣 =40

𝑠𝑒𝑐× 0.8 𝑚

v = 32 m/s

Example Problem #4: Finding

wavelength

The speed of a sound wave is 343 m/s and has a frequency of 500 Hz.

What is the length of the wavelength?

λ =343 𝑚

𝑠𝑒𝑐×

𝑠𝑒𝑐

500

λ = 0.686 m

λ =𝑣

𝑓

λ =343𝑚/𝑠

500 𝐻𝑧

λ =343𝑚/𝑠

500/𝑠𝑒𝑐

Example Problem #5: Finding the frequency

The wavelength of a wave is 0.002 m and it has a wave speed of

0.05 m/s. What is the frequency of that wave?

f =0.05𝑚

𝑠𝑒𝑐×

1

0.002𝑚

f = 25 Hz

f = 𝑣

λ

f = 0.05 𝑚/𝑠

0.002𝑚

f = 25/second