{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

6B_Chapter_14_GG

# 6B_Chapter_14_GG - Chapter 14 Superposition and Standing...

This preview shows pages 1–13. Sign up to view the full content.

Chapter 14 Superposition and Standing Waves

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Superposition Principle If two or more traveling waves are moving through a medium and combine at a given point, the resultant position of the element of the medium at that point is the sum of the positions due to the individual waves Waves that obey the superposition principle are linear waves – In general, linear waves have amplitudes much smaller than their wavelengths
Superposition Example Two pulses are traveling in opposite directions The wave function of the pulse moving to the right is y 1 and for the one moving to the left is y 2 The pulses have the same speed but different shapes The displacement of the elements is positive for both When the waves start to overlap (b), the resultant wave function is y 1 + y 2 The shapes of the pulses remain unchanged

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Superposition in a Stretch Spring Two equal, symmetric pulses are traveling in opposite directions on a stretched spring They obey the superposition principle
Superposition and Interference Two traveling waves can pass through each other without being destroyed or altered – A consequence of the superposition principle The combination of separate waves in the same region of space to produce a resultant wave is called interference

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Types of Interference Constructive interference occurs when the displacements caused by the two pulses are in the same direction – The amplitude of the resultant pulse is greater than either individual pulse Destructive interference occurs when the displacements caused by the two pulses are in opposite directions – The amplitude of the resultant pulse is less than either individual pulse
Destructive Interference Example Two pulses traveling in opposite directions Their displacements are inverted with respect to each other When they overlap, their displacements partially cancel each other

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Superposition of Sinusoidal Waves Assume two waves are traveling in the same direction, with the same frequency, wavelength and amplitude The waves differ in phase y 1 = A sin ( kx - ω t ) y 2 = A sin ( kx - ω t + φ ) y = y 1 + y 2 = 2 A cos ( φ /2) sin ( kx - ω t + φ /2)
Superposition of Sinusoidal Waves, cont The resultant wave function, y , is also sinusoidal The resultant wave has the same frequency and wavelength as the original waves The amplitude of the resultant wave is 2 A cos ( φ / 2) The phase of the resultant wave is φ /2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Sinusoidal Waves with Constructive Interference • When φ = 0, then cos ( φ /2) = 1 The amplitude of the resultant wave is 2 A – The crests of one wave coincide with the crests of the other wave The waves are everywhere in phase The waves interfere constructively
Sinusoidal Waves with Destructive Interference • When φ = π , then cos ( φ /2) = 0 – Also any even multiple of π The amplitude of the resultant wave is 0 – Crests of one wave coincide with troughs of the other wave The waves interfere destructively

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Sinusoidal Waves, General
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}