Concepts : Destructive waves vs. equilibrium

In summary, two identical upward and downward pulses are propagating in opposite directions on a stretched string. When they overlap completely, the string is at equilibrium with zero displacement everywhere. However, there is still energy present in both waves, with maximum kinetic energy and zero potential energy at this instant. This situation differs from true equilibrium, where both kinetic and potential energy are zero.
  • #1
Essenar
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Homework Statement


An upward and downward pulse, otherwise identical in shape are propagating in opposite directions along a stretched string. At the instant they overlap completely, the displacement of the string is exactly zero everywhere. How does this situation differ from true equilibrium?
HINT: Where is the wave energy?


Homework Equations





The Attempt at a Solution


I'm assuming that for wave 1, amplitude = +A and for wave 2, amplitude = -A.
y1(x, t) = A1 cos((k1)x - (w1)t + phi1)
y2(x, t) = -A1 cos ((k2)x + (w2)t + phi2)
No phase change so phi's drop, +/- symbols to indicate opposite directions. Now, while they cancel, I'm assuming that even if there is 0 displacement, there is still energy in both waves. However I'm having trouble proving it.
Thanks guys and I hope I posted this properly.
 
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  • #2
The spring has both kinetic and potential energy. At the instant the displacement is zero along the whole spring, PE=0 and KE is maximum.

ehild
 

FAQ: Concepts : Destructive waves vs. equilibrium

1. What is the difference between destructive waves and equilibrium?

Destructive waves are ocean waves that have a strong backwash and tend to erode the shoreline, while equilibrium refers to a state of balance where the amount of sediment added to the beach equals the amount removed by erosion. In other words, destructive waves cause erosion while equilibrium maintains the beach's shape and size.

2. How do destructive waves form?

Destructive waves form when strong winds blow over a long distance of open water, creating large and steep waves. These waves have a short wavelength and high height, making them more forceful and capable of causing erosion.

3. What factors can disrupt the equilibrium of a beach?

There are several factors that can disrupt the equilibrium of a beach, including changes in sea level, storms, and human activities such as construction or sand mining. These disturbances can alter the balance between sediment input and removal, leading to erosion or accretion of the beach.

4. How can we prevent destructive waves from causing erosion?

One way to prevent destructive waves from causing erosion is by building structures such as seawalls or breakwaters to dissipate their energy before reaching the shoreline. Additionally, beach nourishment projects, where sand is added to the beach, can help maintain the equilibrium and reduce erosion.

5. What are the potential impacts of an imbalanced beach equilibrium?

An imbalanced beach equilibrium can have various impacts, such as loss of beachfront property, damage to coastal infrastructure, and loss of important habitats for marine life. It can also make the shoreline more vulnerable to erosion during storms and sea level rise.

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