14-9,14-10

Created by Rosalie Ho

14-9 Superposition of waves

Have you ever wondered how you can identify the different instruments playing in a concert at the same time ?

This is because of the Principle of Superposition of Waves

Principle of Superposition of Waves

The net force at a point= sum of all forces

Resultant displacement of the point=sum of displacement (+/-) of all the waves at that point

Waves don’t affect other waves’ interaction with the medium

Waves passes through each other unaffected

Terms Resultant Wave

Wave obtained by adding all the component waves

Superposition

Process of adding waves to produce a wave that is the sum of all waves

Interference

2 or more waves combining to produce a resultant wave

14-10 Interference of Waves

Travelling in the Same direction There are 2 waves

Wave 1 has a phase constant of 0 and wave 2 has a phase constant of Φ

The different of the phases is Φ-0=Φ

Wave functions of given 2 waves Wave function 1 :D1(x,t)= Asin(kx-ωt)

Wave function 2 :D2(x,t)=Asin(kt-ωt+Φ)

Or

Wave function2:D2(x,t)=Asin[k(x+Φ/k)-ωt]

Resultant wave

Eqn of resultant wave of wave 1 & 2:

D(x,t)=2Acos(Φ/2)sin(kx-ωt+Φ/2)

Resultant amplitude of resultant wave from wave 1 & 2 = 2Acos(Φ/2)

Constructive and destructive interference

Constructive : When the phase difference of 2 waves are in a multiple of 2pi rad

Destructive: when the phase difference of 2 waves are in a multiple of pi rad , they will cancel each other out

Activity

a)Sketch the resultant wave of the following waves

b) Is it constructive or destructive interference?

c)Calculate the resultant amplitude

Question 1

Question 2

Answers Question 1

Answers Question 1

b) Constructive

c) 40m

Answers Question 2

Answers Question 2

b) Destructive

c) 5m