Harmonic WavesLEARNING OBJECT

LG2- ALISON WU

What is a Harmonic Wave?

If a wave is undergoing harmonic motion it is considered a harmonic wave. Simple harmonic motion is the type of periodic motion in which the restoring force is directly proportional to the displacement

It is also known as a sinusoidal wave (a sin graph)

It has a smooth repetitive oscillation

Which graph represents a harmonic wave?

a) b) c)

Solution

A)

Since a harmonic wave is described by a sine (or a cosine) function, its properties are determined by the amplitude (A), it’s wavelength (λ) and it’s period (T)

Characteristics of a Harmonic wave

Amplitude: Corresponds to the maximum displacement from the equilibrium position of any element. Amplitude is always a positive quantity.

Wavelength: The shortest distance over which a wave shape repeats is called the wavelength. Represented by the symbol lambda (λ)

Wave number: the reciprocal of the wavelength

Period: the time for a particle make one complete cycle T=1/f

Frequency: the number of wave cycles passing a fixed point of the medium in one section

Phase shift (φ) : a horizontal shift by how many units the "starting point" (0,0) of a standard sine curve, y = sin(x), has moved to the right or left.

What is the amplitude of the graph?

a)-0.5b)1c)0.5d)0.25

What is the wave number of the graph?

a)pib)pi/2c)1/2d)2

What is the phase shift?

a)2pib)2pi/3c)pi/3d)pi

Solutions

1. c) 0.5

2. d) 2

3. b)2pi/3

Speed of the Wave

To calculate the speed of the wave you multiply the wavelength of the graph to the frequency.

Find the angular frequency when the wave has a velocity of 100m/s, a wave number of 2.

a) 50

b) 0

c) 200

d) 30

Solutions

1. plug the numbers into the equation, we know that wavelength is equal to 2pi/k and frequency is equal to w/2pi

2. Sub those equations into the original formula and you will get

v= w/k

3. rearrange to solve for angular frequency

w=vk

4. plug in your number

5.w=100*2

w=200

c)

If the frequency increased what would happen to the velocity?

a) it remains constant

b) it would decrease

c) it would increase

Solution

C) it would increase

All three factors are in direct correlation so if the frequency increased the velocity would increase to.