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 = 0.090 sin ( xpi/12 + 5pit)

(a) Determine the transverse speed at t = 0.260 s for an element of the string located at x = 1.30 m.where x and y are in meters and t is in seconds.

(b) Determine the transverse acceleration at t = 0.260 s for an element of the string located at x = 1.30 m.
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

y = 0.090 sin ( xpi/12 + 5pit)

dy/dt = 0.09*5pi cos(xpi/2+5pit)

t = 0.260

x = 1.30

velocity = 0.9942 m/s

Determine the transverse acceleration at t = 0.260 s for an element of the string located at x = 1.30 m.
m/s2

dy/dt = 0.09*5pi cos(xpi/2+5pit)

d^2y/dt^2 = -0.09 (5pi)^2 (sin(xpi/2+5pit))

a = 15.11 m^2/s

What is the wavelength of this wave?
m

pi/12

What is the period of this wave?
s

5pi

What is the speed of propagation of this wave?
m/s

0.090

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