Question

The function y(x, t) = (20.0 cm) cos(πx - 17πt), with x in meters and t in seconds, describes a wave on a taut string. What is the transverse speed for a point on the string at an instant when that point has the displacement y = +17.0 cm?

Number

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Units

Choose the answer from the menu in accordance to the question statement This answer has no units° (degrees)mkgsm/sm/s^2NJWN/mkg·m/s or N·sN/m^2 or Pakg/m^3gm/s^3times

the tolerance is +/-2%

Answer 1

Given transverse wave equation is:

y(x, t) = 20.0 cm*cos (x - 17t)

Speed of transverse wave will be given by:

V(x, t) = d(y(x, t))/dt = d[20.0 cm*cos (x - 17t)]/dt

V(x, t) = d[0.2*cos (x - 17t)]/dt

V(x, t) = 0.2*(-17*)*(-sin (x - 17t))

V(x, t) = 3.4*sin (x - 17t)

Now when displacement of a point on the string is y = 17.0 cm, then

y(x, t) = 20.0 cm*cos (x - 17t) = 17.0 cm

cos (x - 17t) = 17.0/20.0

(x - 17t) = arccos (17.0/20.0) = 0.5548 rad

Now transverse speed of that point will be:

V(x, t) = 3.4*sin (x - 17t)

V(x, t) = 3.4*pi*sin (0.5548 rad)

V(x, t) = 5.63 m/s

(If need then you can use V(x, t) = 563 cm/s)

Let me know if you've any query.