A long string carries a wave; a 5.40-m segment of the string contains three comp

Question

A long string carries a wave; a 5.40-m segment of the string contains three 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 16.0 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.)
y =

Explanation / Answer

Let y = lambda the wavelength A (amplitude) = .16 / 2 = .08 m y = 5.4 / 3 = 1.8 m Y = A sin k (x - v t) to not confuse y and Y k = 2 * pi / y = 3.49 Y = .08 sin [3.49 (x - v t)] Also, v = f y = 45 * 1.8 = 81 Y = .08 sin [3.49 (x - 81 t)]

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