In the diagram below a wave is shown at an instant in time (t = 0.0 s). The wave
ID: 1613538 • Letter: I
Question
In the diagram below a wave is shown at an instant in time (t = 0.0 s). The wave has a frequency of 2.0 Hz and is traveling to the right along a copper wire. Density of copper is 8.90 times 10^3 kg/m^3. a. What is the wavelength of this wave? b. What is the velocity of the wave? c. What is the amplitude of wave? d. Express the displacement (D (x, t)) of this wave as a function of x (in meters) and t (in seconds). e. What is the intensity of this wave? f. Write down the equation (displacement) of a wave with the same amplitude, frequency, and wavelength of this wave except that it's travelling to the left.Explanation / Answer
(A) wavelenhth = distance between consecutive nodes
wavelength = 24 cm
(b) f = 2 Hz
v = wavelength f = (0.24 m ) (2 Hz)
= 0.48 m/s
(C) Amplitude = 6 cm
(D) w = 2 pi f = 4 pi rad/s
D(x, t) = A sin(kx - wt)
k = 2pi/lambda = 2 pi / 0.24 = 8.33 pi
D(x,t) = 6 cm sin(8.33pi x - 4 pi t)
(e) I = rho w^2 A^2 v / 2
I = (8.90 x 10^3) (4pi)^2 (0.06^2) (0.48) /2
I = 1214.3 W/m^2
(F) D(x,t) = 6 cm sin(8.33pi x + 4 pi t)