A long string carries a wave; a 5.60-m segment of the string contains four compl

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

peak tp valley distance = 12 cm

so A = 6 cm = 0.06 m

w = 2*pi*f = 2*3.14*45 = 282.6 rad/s

there are 5 waves in 5.60 m long segment

so lambda = 5.60/5 = 1.12 m

wave number k = 2*pi/lambda = 2*3.14/1.12

k = 5.60 rad/m

wave traveling in the positive x direction

y(x,t) = A*sin(w*t + k*x)

y(x,t) = 0.06*sin(282.6*t + 5.60*x)

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