How Do Two Superposed Waves Result in Points of Zero Displacement?

In summary, in this conversation, the two given waves y1 and y2 are combined to find the resultant displacement and the expression of x where the displacement is always zero. Using the equations for sine and cosine, the expression for the resultant displacement is found to be y=2Ysin(kx)cos(-wt). The second part of the problem asks for the expression of x when the displacement is always zero, which is found to be x=n*pi/k, where n is an integer.
  • #1
socoil23
4
0

Homework Statement


given 2 waves y1=Ysin(kx-wt): y2=Ysin(kx+wt).
derive expression of resultant displacement and expression of x(for resultant) where displacement always zero


Homework Equations


y=y1+y2
sinA+sinB=2sin((A+B)/2)cos((A-B)/2)


The Attempt at a Solution


i solved first part:y= 2Y sin (kx) cos (-wt)
but i don't understand the 2nd part. does it mean y=0 when sin kx=0? mean x=0?
 
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  • #2
Is x = 0 the only value of x at which sin(kx) = 0?
 
  • #3
I had figure it out.displacement is directly related to sin kx.displacement is Zero when kx equal to n*pai
where n is integer.displacement always zero when x = n*pai/k.
 

FAQ: How Do Two Superposed Waves Result in Points of Zero Displacement?

What is the principle of superposition?

The principle of superposition is a fundamental concept in physics and engineering that states that when two or more waves or fields interact, the resulting wave or field is the algebraic sum of the individual waves or fields.

How does the principle of superposition apply to sound waves?

In sound waves, the principle of superposition explains how multiple sound waves can overlap and combine to form a new, resulting sound wave. This is how we are able to hear different instruments and voices simultaneously when listening to music.

What is the significance of the principle of superposition in quantum mechanics?

In quantum mechanics, the principle of superposition allows for the existence of particles in multiple states at the same time. This is known as quantum superposition and is a fundamental concept in understanding the behavior of subatomic particles.

Can the principle of superposition be applied to other fields besides physics?

Yes, the principle of superposition can be applied to other fields such as electrical engineering, where it explains how multiple electrical signals can combine to create a resulting signal. It can also be applied to fields such as finance and economics, where the principle of superposition can be used to analyze the effects of multiple variables on a system.

What are some real-world examples of the principle of superposition?

One example of the principle of superposition in action is in the formation of interference patterns in water waves or light waves. Another example is the use of superposition in signal processing, such as in noise-cancelling headphones. Additionally, the principle of superposition is used in MRI technology to create images by analyzing the superposition of multiple magnetic fields.

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