A long string carries a wave; a 5.60-m segment of the string contains four compl
ID: 1510878 • Letter: A
Question
A long string carries a wave; a 5.60-m segment of the string contains four complete wavelengths and has a mass of 180 g. The string vibrates sinusoidally with a frequency of 45.0 Hz and a peak-to-valley displacement of 12.0 cm. (The "peak-to-valley" distance is the vertical distance from the farthest positive position to the farthest negative position.)
(a) Write the function that describes this wave traveling in the positive x direction. (Use the following as necessary: x and t. x is in meters and t is in seconds. Enter your numerical coefficients to four significant figures.)
y = ?
(b) Determine the power being supplied to the string.
? W
Explanation / Answer
Wavelength = 5.6/4=1.4 m
w = 2f = 90
a) the function that describes this wave traveling in the positive x direction
Is given as y=Asin(wt+)
Where A=Amplitude,w=angular velocity, =phase-angle
A=peak-to-valley displacement of 12.0 cm/(2)
y = 0.06 sin wt = 0.06 sin 90 t
(b)Power = 1/2 . w^2 . A^2 . density . wavespeed
= 0.5 . (90)^2 . 0.06^2 . (0.18 / 5.6) . (45 . 1.4)
Calculate the value of Power using these values.
That will be in watts