A transverse wave on a string is described by the following wave function. y = 0

Question

A transverse wave on a string is described by the following wave function. y = 0.105 sin ? 10 x + 5?t where x and y are in meters and t is in seconds. (a) Determine the transverse speed at t = 0.130 s for an element of the string located at x = 1.70 m. Given the equation for the vertical position of elements of the string as a function of time, how do you determine the velocity of those elements as a function of time? m/s (b) Determine the transverse acceleration at t = 0.130 s for an element of the string located at x = 1.70 m. Given the equation for the vertical position of elements of the string as a function of time, how do you determine the velocity of those elements as a function of time? m/s2 (c) What is the wavelength of this wave? m (d) What is the period of this wave? s (e) What is the speed of propagation of this wave? m/s

Explanation / Answer

A normal wave equation would be y=Asin(kx-wt) speed of the wave= dy/dt=0.105*5cos(10x+5t) but given t and x,substitute them acceleration is d2y/dt2=-0.105*5*5sin(10x+5t) wavelength=2*pi/10 period=2*pi/5 speed of propagation=5/10=0.5

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