The wave function for a traveling wave on a taut string is (in SI units) The wav

Question

The wave function for a traveling wave on a taut string is (in SI units)

The wave function for a traveling wave on a taut string is (in SI units) y(x,t) = 0.395 sin (15pit ? 1pix + pi 4 ) (a) What are the speed and direction of travel of the wave? speed m/s direction ---Select--- positive x-direction positive y-direction positive z-direction negative x-direction negative y-direction negative z-direction (b) What is the vertical position of an element of the string at t = 0, x = 0.115 m? m (c) What is the wavelength of the wave? m (d) What is the frequency of the wave? Hz (e) What is the maximum transverse speed of an element of the string? m/s

Explanation / Answer

position y(x,t) = 0.395 sin(15t 1x + /4)
compare this y(x,t)= A sin(wt-kx+) we get

amplitude A= 0.395 m

angular frequency w = 15 rad / s

propagation constant k = rad / m

epoch = /4

(a) the speed of the wave v = w / k

v = 15 m / s

direction is positive x-direction

(b) he vertical position of an element of the string at t = 0, x = 0.115 m is

y = 0.395 sin[(15*0)-(*0.115) +/4]

= 0.36 *0.9114

= 0.36 m

(c) the wavelength of the wave = 2 / k = 2 m

(d) the frequency of the wave f = w/ (2*)

= 7.5 Hz

(e) The maximum transverse speed of an element of the string = Aw = 18.61m/s

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