Webpage title: Calculating Distance Between Nodes in a Standing Wave on a String

  • Thread starter Thread starter gleeman
  • Start date Start date
  • Tags Tags
    Translation Waves
AI Thread Summary
The discussion centers on calculating the distance between adjacent nodes in a standing wave formed by the superposition of two traveling waves, represented by the equations y1=Asin(ωt−kx) and y2=Asin(ωt+kx). The initial confusion arises from understanding how the distance between nodes relates to the wave equations. It is clarified that the distance between two nodes is derived from the relationship 2π/k, leading to the conclusion that the distance between adjacent nodes is π/k. The phase shift of the waves is also noted as a key factor in determining this distance. The final answer emphasizes the connection between wave properties and their spatial characteristics.
gleeman
Messages
6
Reaction score
0
The question is: "Two traveling waves are superposed on the same string. Waves are y1=Asin (ωt−kx) and y2=Asin(ωt+kx).The distance between adjacent nodes of the resulting standing wave is: "

This is the question I have tried to solve.
I know that the distance between two nodes is 2pii. Then I do not know how to proceed.

The answer is pii/k,
but I do not know how it is obtained.

Please, do not hesitate to reply if you know why the answer is pii/k.

Thank you in advance!
 
Physics news on Phys.org
-kx and +kx is the phase shift of the two waves. How far apart are the two waves then? How can you relate this to the period and the distance, x?
 
Thank you, you solved this question as 2pii=2kx => Distance(x)=pii/k.
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Standing wave transverse motion and amplitude
Replies
5
Views
2K
How Do You Calculate the Energy of a Standing Wave?
Replies
21
Views
3K
Wave equation, wavelenght not given
Replies
6
Views
2K
Finding Nodes in a Standing Wave at 800 Hz
Replies
4
Views
4K
What is the velocity dependence in the equation of a standing wave?
Replies
13
Views
13K
Standing Wave Nodes and Interference on a Stretched String
Replies
1
Views
2K
Velocity and frequency of standing waves, number of nodes
Replies
1
Views
4K
What Is the Distance Between Adjacent Nodes in Superimposed Waves?
Replies
3
Views
7K
Amplitude and Velocity of Component Waves
Replies
5
Views
6K
Calculating the length of a string from a standing wave
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top