4. 1/7 points Previous Answers HRWe 16.P010. My Notes Ask Your Teacher The equat

Question

4. 1/7 points Previous Answers HRWe 16.P010. My Notes Ask Your Teacher The equation of a transverse wave traveling along a very long string is given by y-5.0 sin(O.017mx+4.2nt), where x and y are expressed in centimeters and t is in seconds. Determine the following values (a) the amplitude (b) the wavelength (c) the frequency Hz (d) the speed cm/s (e) the direction of propagation of the wave o -y f) the maximum transverse speed of a particle in the string cm/s (g) the transverse displacement at x-3.5 cm when t = 0.26 s 0.26 s Do you see how to get the transverse velocity u by differentiating the displacement equation? What is the maximum value of the transverse speed? Given values of x and t, can you find the displacement y?

Explanation / Answer

here,

y = 5 * sin(0.017 *pi*x + 4.2 * pi * t)

general equation

y = A * sin(kx + w*t)

so,

(A)

the amplitude is 5 cm

(B)

k = 0.017 * pi

lamda = 2*pi /k

lamda = 117.65 m

the wavelength is 117.65 m

(C)

w = 4.2 pi

frequency , f = w/2pi

f = 2.1 Hz

(D)

A positive sign means the wave is traveling in the -x direction.

so , the direction of propogation is in -x direction

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