How Do You Calculate the Speed and Deflection of a Wave on a String?

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SUMMARY

The discussion focuses on calculating the speed and deflection of a transverse wave on a string, described mathematically by the equation Y(x,t) = A cos [k(x-vt)]. Key calculations include determining the maximum transverse speed (vy) of a particle and its relationship to wave propagation speed. Given parameters include an amplitude of 0.300 cm, wavelength of 12.0 cm, and a wave speed of 6.00 cm/s, leading to the calculation of frequency and deflection at specific time and position values.

PREREQUISITES
  • Understanding of wave equations and parameters (amplitude, wavelength, speed)
  • Knowledge of calculus for derivatives (to find transverse speed)
  • Familiarity with the relationship between wave speed, frequency, and wavelength (v = f λ)
  • Basic physics concepts related to wave motion
NEXT STEPS
  • Calculate the frequency of a wave using the formula v = f λ
  • Explore the concept of wave propagation and transverse speed equality
  • Review calculus techniques for finding derivatives in wave motion
  • Study examples of wave deflection calculations in different media
USEFUL FOR

Students in physics, educators teaching wave mechanics, and anyone involved in understanding wave behavior on strings.

saksham
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Help Needed! Waves, Urgent!

******Mathematical description of a wave:******

A transverse wave on a string can be described by:
Y(x,t)= A cos [k(x-vt)]

a) Find the maximum transverse speed vy of a particle of the string. Under that circumstances is it equal to the propagation speed of the wave?

b) The wave has an amplitude of 0.300 cm, wavelength 12.0 cm, and speed 6.00 cm/s. What is its frequency? What is the deflection of a particle of the string at time t = 5 s and position x = 10 cm?

Please help me out! I have deadline tonight.

Physicist.
 
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Hint for a: Find the transverse speed by taking the derivative.

Hint for b: Use the wave equation: [itex]v = f \lambda[/itex].

Hint for both: Crack open that textbook! :smile:
 
Under what circumstances are the traverse speed and speed of propagation equal?
 

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