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

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To calculate the speed and deflection of a wave on a string, the wave can be described using the equation Y(x,t) = A cos[k(x-vt)]. The maximum transverse speed of a particle can be determined by taking the derivative of this equation, and it is only equal to the wave's propagation speed under specific conditions. Given an amplitude of 0.300 cm, a wavelength of 12.0 cm, and a speed of 6.00 cm/s, the frequency can be calculated using the wave equation v = fλ. Additionally, the deflection of a particle at a specific time and position can be found by substituting the values into the wave equation. Understanding these calculations is essential for solving wave-related problems effectively.
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******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: v = f \lambda.

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