A fixed string in the third harmonic

  • Thread starter Thread starter TFM
  • Start date Start date
  • Tags Tags
    Harmonic String
Click For Summary

Homework Help Overview

The discussion revolves around a physics problem involving a string vibrating in its third harmonic. The string has fixed ends, a wave speed of 195 m/s, and a frequency of 230 Hz. Participants are tasked with calculating the amplitude at a specific point on the string, given the amplitude at an antinode and the distance from one end of the string.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the meaning of the third harmonic and its implications for the wave's properties. There are attempts to calculate the wavelength and identify nodes and antinodes. Questions arise regarding the correct application of formulas and the significance of time in the amplitude calculation.

Discussion Status

The discussion is active, with participants providing guidance on the use of relevant equations and clarifying concepts. Some participants express uncertainty about their calculations and seek confirmation on their approaches, while others offer corrections and suggestions for further exploration.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information available and the methods they can use. There is an emphasis on understanding the relationship between amplitude, position, and time in the context of wave motion.

  • #31
Using:

v(x,t) = A_S_W \omega sin(\frac{\pi }{2}) cos(0)

gives me: 5.33

then

a(x,t) = A_S_W \omega ^2 sin(\frac{\pi }{2}) sin(\frac{\pi }{2})

gives me: 7700

Both of which are right. I disagree with mastering physics - if you diffentiate cos, it gives you minus sin:

a(x,t) = -A_S_W \omega ^2 sin(\frac{\pi }{2}) sin(\frac{\pi }{2}) giving -7700, which it said was wrong?

Many Thanks,

TFM
 
Physics news on Phys.org
  • #32
Indeed you do get minus sin, but -7700 would be the maximum deceleration, and it asks for the maximum acceleration. At least that's what I tell myself.

Thanks for your help with the period, I think I was having a mental bock.
 
  • #33
Have you got the right answer yet for the time, as I have left the thread marked unsolved until you have finished.:smile:

I think I was having a mental bock.

Don't worry, I think it happens to all of us from time to time!

TFM
 
  • #34
Yeah, I got in the end. Thanks for that :smile:.

By the way are you still working on the 'instantaneous power in a standing wave' problem? Sketching the graphs is quite tricky.
 

Similar threads

Waves and vibrations on a string
  • · Replies 2 ·
Replies
2
Views
2K
Calculating Mass of a Vibrating String Using Known Quantities
  • · Replies 10 ·
Replies
10
Views
2K
Effect of temperature on vibrational frequency of a violin string
  • · Replies 5 ·
Replies
5
Views
2K
Standing Waves On Strings: Harmonic and Frequency Problem
  • · Replies 2 ·
Replies
2
Views
4K
Which Frequency is NOT Possible for a Vibrating String?
  • · Replies 5 ·
Replies
5
Views
2K
Standing waves on a fixed string
  • · Replies 3 ·
Replies
3
Views
5K
Find two lowest frequencies standing wave
  • · Replies 5 ·
Replies
5
Views
6K
Maximum and minimum transverse speeds at an antinode
  • · Replies 6 ·
Replies
6
Views
4K
Calculating the length of a string from a standing wave
  • · Replies 4 ·
Replies
4
Views
2K
Violin frequencies and harmonics
  • · Replies 2 ·
Replies
2
Views
4K