Question

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x,t)=(2.30mm)cos[(6.18rad/m)x+(702rad/s)t]. Being more practical, you measure the rope to have a length of L and a mass of 0.00333 kg.

Part A Determine the amplitude. Express your answer with the appropriate units. A=

Part B Determine the frequency. Express your answer with the appropriate units. f=

Part C Determine the wavelength. Express your answer with the appropriate units. λ=

Part D Determine the wave speed. Express your answer with the appropriate units. v=

Part E Determine the direction the wave is traveling. Determine the direction the wave is traveling. −x−direction +x−direction

Part F Determine the tension in the rope. Express your answer with the appropriate units.

Part G Determine the average power transmitted by the wave. Express your answer with the appropriate units.

Answer 1

Given wave equation of traveling wave is:

y(x, t) = (2.30 mm)*cos (6.18*x + 702*t)

Standard equation: y(x, t) = A*cos (kx + wt)

Part A.

A = Amplitude = 2.30 mm

Part B.

Angular frequency will be:

w = 2*pi*f

f = w/(2*pi) = 702/(2*pi)

f = 111.7 Hz

Part C.

wave number is given by:

k = 2*pi/

= wavelength = 2*pi/6.18

= 1.02 m

Part D.

wave speed is given by:

V = w/k

V = 702/6.18

V = 113.59 m/s

Part E.

Since there is positive sign between 'kx' and 'wt', so that indicates that wave will be traveling in -ve x-direction

negative x-direction

Part F.

Tension in the rope will be given by:

We know that

V = wave speed = sqrt (T/)

T = *V^2 = m*V^2/L

= mass per unit length = m/L

Now here please comment below the value of L, which is missing in the given question, OR use above expression to calculate.

Part G.

Average power transmitted by the wave is given by:

P_avg = (1/2)*sqrt (*T)*w^2*A^2

Again will need value of L.

Comment below the value of length of string.

Let me know if you've any query.