A sinusoidal wave train is moving along a string. The equation giving the displacement as a function of position and time is
Y(x, t) = 0.12 sin 8$\pi$(t - x/50),
Where the units are SI. For a particle at x = 5 m when t = 2.4 s, the velocity of the particle is
A) 3.7 cm/s
B) 27 cm/s
C) 93 cm/s
D) 1.6 m/s
E) 3.0 m/s

Question

Quizplus · Accepted Answer

We can find the velocity of the particle by taking the derivative of the displacement equation with respect to time:

v(x,t) = (∂Y/∂t) = -0.12*8π/50 cos(8π(t-x/50))

Plugging in x = 5 m and t = 2.4 s, we get:

v(5,2.4) = -0.12*8π/50 cos(8π(2.4-5/50)) = -0.93 m/s

Note that the velocity is negative because the wave is moving to the right (positive x direction), while the particle at x = 5 m is moving to the left (negative x direction).

To convert to cm/s, we multiply by 100:

v(5,2.4) = -93 cm/s ≈ -93.3 cm/s

The closest answer is C, 93 cm/s.

A Sinusoidal Wave Train Is Moving Along a String π\piπ (T - X/50), Where the Units Are SI

A Sinusoidal Wave Train Is Moving Along a String $\pi$ (T - X/50),
Where the Units Are SI