Waves

Question 1

Define Wave

Answer 1

a travelling disturbance that transports energy but not matter

Question 2

What are the 4 types of waves?

Answer 2

Mechanical waves: these are waves that are a disturbance of some material medium.

Electromagnetic waves: these include all the colours of the rainbow in visible late, but also an entire spectrum of waves including gamma rays, x-rays, UV rays, infrared etc. Whats different about these are they don’t require a material medium. The oscillations of an electric and magnetic field can travel through a vacuum.

Matter waves: the waves associated to electrons, protons and other fundamental particles.

Gravitational waves: these waves are disturbances of spacetime itself

Question 3

How can you categorise waves in terms of direction of disturbance?

Answer 3

Longitudinal waves: these waves differ in the sense that if this is the direction of wave propagation then the wave oscillation or disturbance is parallel to the wave propagation.
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For example: Light, or electromagnetic waves, would be an example of transverse waves. Sound on the otherhand, is longitudinal.

Question 4

What are the 3 shapes of waveforms (shape of wave)?

Answer 4

A single disturbance being sent down the string, would be called a wave pulse.

continuous wave which results from on going periodic disturbances

The intermediate case that lies between these two extremes is called a wave packet or a wave train. This is a periodic disturbance that only lasts for a finite amount of time.

Question 5

What are the properties of waves and their formula (if there is one)?

Answer 5

The maximum amount this wave has displaced in the peaks of the wave. This gives me the amplitude, which we usually denote with the letter capital A. In most cases, this amplitude will be measured in meters (m).

The distance between the points on the wave when the pattern starts repeating, this length is referred to as the wavelength, denoted by the Greek letter λ. It is also measured in the S.I. unit of metres (m).

How long it takes before one whole cycle has occurred. This time that it took, is referred to as the period denoted by a capital T usually, and being time is unsurprisingly measured in the S.I. unit of seconds (s).

How many cycles pass through the origin within a particular unit of time, then the amount of cycles that occurred in that time is called the frequency of the wave. A lower case f is often used for that and it is measured in Hertz (Hz). There is actually a fairly important relationship between frequency and period and that is: f = 1 / T

How quickly it is travelling, generally referred to as the wave speed which we make use of the letter v for: v = λ / T = λ*f

Question 6

What is the formula for horizontal translation?

Answer 6

y(x) = f(x + ϕ), where the function f is y(x, t) = cos(x + ϕ(t)) - a cosine function

Question 7

What is the formula for vertical dilation?

Answer 7

y(x, t) = A cos(x + ϕ(t))

Question 8

What is the formula for horizontal dilation?

Answer 8

y(x, t) = A cos ((2π / λ) x + ϕ(t)), where (2π / λ) x + ϕ(t) is also known as the phase of a wave

Question 9

What is the formula for angular frequency?

Answer 9

ω = 2πf

Question 10

What is the formula for wave number?

Answer 10

k =2π / λ

Question 11

What is the overall formula for the function of a wave?

Answer 11

y(x, t) = A cos(kx + ωt)

Question 12

What is the formula for kinetic energy?

Answer 12

dK =1/2 (dm)v^2

Question 13

What is the formula for average rate?

Answer 13

(dK/dt)avg = 1/4 µvω^2A^2

Question 14

What is the formula for elastic potential energy?

Answer 14

(dK/dt)avg = (dU/dt)avg

Question 15

What is the formula for average power?

Answer 15

P =1/2 µvω^2A^2

Question 16

Define intensity and its formula

Answer 16

The rate at which the wave carries energy across a unit area perpendicular to the wave propagation -> I = P/A

That is the intensity of a wave drops off at a rate of the square of the distance from the source, because you are spreading the same energy over more area

Question 17

Define Constructive and Destructive Interference

Answer 17

This addition of amplitudes, where the resultant wave is larger that either of the original two waves, is called constructive interference

The amplitudes then cancel each other when they add. This concept
is known as destructive interference.

Superposition principle

Question 18

Define Beats

Answer 18

There is the quick underlying frequency that our ears will associate with a particular pitch. But over the top of that is this longer period of oscillation that has been indicated in red in the figure. That has an affect on the amplitude of our sound. Amplitude in sound is related to loudness. And that is what gives us the ‘wah wah’ affect. The beats.

The superposition principle just tells us the overall wave is derived from simply adding the two waves together.

It means the amplitude itself is not constant. It is in fact oscillating in time.

The underlying frequency however, once the two angular frequencies are equal, then the half factor corrects it to a frequency of one ω, which is why it sounds the correct pitch to us once its tuned at the en

Question 19

What is reflection?

Answer 19

REFER TO EXAMPLE:

This must mean the reflected wave is going to have to be destructively interfering at this point. What does that mean? When the wave reflects, because it has to destructively interfere at the reflection point, it must be inverted to the original waveform.

The wave energy, when it hits here, will still need to reflect as it can’t continue past this point, but this time it doesn’t need to destructively interfere at the reflection point. This time when it reflects, it doesn’t invert. Now if I hit pause in time when the wave hits the free end you’ll discover the amplitude is double. That is because we have at this point the original wave and the reflected wave constructively interfering with each other

Question 20

What is a standing wave?

Answer 20

It is instead fluctuating in time. Whereas the sin(kx) part is the sinusoidal wave. Notice though that it does not rely on time, it is purely stationary. Meaning this wave is not travelling, it is stuck in place. So now all movement is gone, this is what we call a standing wave.

Question 21

What are nodes and antinodes?

Answer 21

Where the x-axis do not move at all. They always stay with zero displacement for all time t. They are called the nodes. Whereas the points of maximum displacement (in between the nodes) that keep moving between peak and trough, are called antinodes.

Question 22

Define fundamental frequency

Answer 22

Being the lowest frequency is knkown as the first harmonic

Question 23

What is the formula for standing wave on a clamped string?

Answer 23

L = (n/2) * λ

Question 24

What is he formula for standing wave on a clamped string on one side?

Answer 24

L = (m/4) * λ

Question 25

What is the doppler effect and its formula?

Answer 25

Frequency, remember, in sound is related to pitch. So you can tell that a source receding from you appears to have a larger wavelength, so a smaller frequency and thus a lower pitch. Things travelling towards you instead sound like a higher pitch. This is called the Doppler effect.

fA = f (1 ± (u/v))

Redshift: In the electromagnetic spectrum, larger wavelengths are on the red side of the spectrum

Blue Shift:If something was moving towards us, then the wavelength would be smaller and it would look bluer than it should be