Actual displacement of a wave particle

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SUMMARY

The discussion focuses on calculating various properties of a wave on a stretched string with specific parameters: amplitude (A) of 0.30 m, angular frequency (ω) of 9.0 rad/s, tension (T) of 4.0 N, and mass per unit length (µ) of 1.250 g/m. The wave velocity is determined to be 56.6 m/s, the frequency of oscillation is calculated as 1.43 Hz, and the wavelength is found to be 39.6 m. The challenge lies in calculating the displacement of the string at a specific position and time, utilizing the equation for vertical displacement, y = A sin(kx - ωt), where k is the wave number.

PREREQUISITES
  • Understanding of wave mechanics and properties
  • Familiarity with the wave equation and trigonometric functions
  • Knowledge of tension and mass per unit length in strings
  • Ability to manipulate angular frequency and its relationship to frequency
NEXT STEPS
  • Learn how to derive the wave number (k) from wavelength (λ)
  • Study the relationship between angular frequency (ω) and frequency (f)
  • Explore the concept of wave displacement using the equation y = A sin(kx - ωt)
  • Investigate the effects of tension and mass per unit length on wave speed in strings
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators and anyone interested in understanding the dynamics of waves on strings.

Jon.G
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Homework Statement


The end of a stretched string is forced to vibrate with a transverse displacement with A= 0.30 m and ω = 9.0 rad s-1. If the tension of the string is T = 4.0 N, and the mass per unit length is µ= 1.250 g m-1, calculate

(a) the wave velocity,

(b) the frequency of oscillation,

(c) the wavelength, and

(d) the displacement of the string at x = 2.0 m from the source at the time t = 100 ms after the oscillation commences.
Assume that the wave is traveling from left to right.

The attempt at a solution
a.) v=√(T/μ) giving me a wavespeed of 56.6 ms-1
b.)ω=2∏f giving me a frequency of 1.43 Hz
c.)v=fλ giving me a wavelength of 39.6 m
d.)This is where I'm stuck :( I would think of using the equation vertical displacement,
y=Asin(kx-ωt) except I don't know how to find k
Any help appreciated.
 
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If you put t=0, then you have y=Asin(kx)
... then when x=0, y=0 right?
... when x=λ, what is y equal to (hint: definition of wavelength)?
... therefore what is kλ equal to?
 

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