A wave on a string,mass per unit length of 0.2 g/cm,travels in the z direction with the string displaced in the x and y directions as described by the equations
x = 5sin(kx - ωt)cm,and
Y = 5cos(kx - ωt)cm.
The wavelength and the wave velocity are γ = 11 cm and v = 6 cm/s respectively.What average power is transmitted along the string?

Question

A wave on a string,mass per unit length of 0.2 g/cm,travels in the z direction with the string displaced in the x and y directions as described by the equations 
x = 5sin(kx - ωt)cm,and
Y = 5cos(kx - ωt)cm.
The wavelength and the wave velocity are γ = 11 cm and v = 6 cm/s respectively.What average power is transmitted along the string?

Quizplus · Accepted Answer

The average power transmitted along the string is given by:$$P = \frac{1}{2} \mu v \omega^2 A^2$$where:* $\mu$ is the mass per unit length of the string* $v$ is the wave velocity* $\omega$ is the angular frequency* $A$ is the amplitude of the waveIn this case, we have:* $\mu = 0.2 	ext{ g/cm} = 2 	imes 10^{-3} 	ext{ kg/m}$* $v = 6 	ext{ cm/s} = 0.06 	ext{ m/s}$* $\omega = \frac{2\pi v}{\lambda} = \frac{2\pi (0.06 	ext{ m/s})}{0.11 	ext{ m}} = 3.49 	ext{ rad/s}$* $A = 5 	ext{ cm} = 0.05 	ext{ m}$Substituting these values into the equation for average power, we get:$$P = \frac{1}{2} (2 	imes 10^{-3} 	ext{ kg/m})(0.06 	ext{ m/s})(3.49 	ext{ rad/s})^2 (0.05 	ext{ m})^2 = 3.5 	imes 10^{-5} 	ext{ W}$$Therefore, the correct answer is A.

A Wave on a String,mass Per Unit Length of 0