What Factors Determine the Characteristics of Standing Waves on a String?

  • Thread starter Thread starter brownniegyal
  • Start date Start date
  • Tags Tags
    String Wave
AI Thread Summary
The standing wave on the string is represented by the equation y(x, t) = 0.086 sin(8πx) cos(64πt), indicating that nodes occur where sin(8πx) equals zero. The smallest values of x for nodes are found at x = 0, 1/8, and 2/8 meters. The period of oscillation for any point on the string is 1/32 seconds, calculated from the cosine term's frequency. The speed of the traveling waves is determined to be 4 m/s, with an amplitude of 0.086 meters. The first three times when all points on the string have zero transverse velocity occur at t = 0, 1/64, and 1/32 seconds.
brownniegyal
Messages
6
Reaction score
0
A standing wave pattern on a string is described by y(x, t) = 0.086 sin (8πx)(cos 64πt), where x and y are in meters and t is in seconds. For x ≥ 0, what is the location of the node with the (a) smallest, (b) second smallest, and (c) third smallest value of x? (d) What is the period of the oscillatory motion of any (nonnode) point? What are the (e) speed and (f) amplitude of the two traveling waves that interfere to produce this wave? For t ≥ 0, what are the (g) first, (h) second, and (i) third time that all points on the string have zero transverse velocity?


Please provide a solution rather than just an answer :) I really appreciate any help!
 
Physics news on Phys.org
A node occurs where there is no net movement of the string. What values of x will make y = 0?
 
Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

(Disclaimer: this is not a HW question. I am self-studying, and this felt like the type of question I've seen in this forum. If there is somewhere better for me to share this doubt, please let me know and I'll transfer it right away.) I am currently reviewing Chapter 7 of Introduction to QM by Griffiths. I have been stuck for an hour or so trying to understand the last paragraph of this proof (pls check the attached file). It claims that we can express Ψ_{γ}(0) as a linear combination of...
View full post »

Similar threads

Length of string in a standing wave
Replies
19
Views
1K
What Is the Amplitude of the Reflected Wave from a String Sewn in a 2D Membrane?
Replies
4
Views
2K
I Standing Waves by Reflection: Losses of the Reflected Wave
Replies
16
Views
2K
Transverse velocity of a standing wave
Replies
2
Views
4K
Determining the ratio of wave amplitudes along a string
Replies
13
Views
3K
Conservation of power in a traveling wave on a string
Replies
9
Views
2K
Determining Steel String Diameter for Standing Wave Node
Replies
1
Views
2K
Waves and vibrations on a string
Replies
2
Views
2K
Propagating waves along a non uniform string.
Replies
1
Views
4K
I Mechanism of Energy Conservation in Zero-Amplitude Sum of EM Waveforms
Replies
13
Views
782

Hot Threads

Recent Insights

Back
Top