A fellow student of mathematical bent tells you that the wave function of a trav

Question

A fellow student of mathematical bent tells you that the wave function of a traveling wave on a thin rope is . Being more practical-minded, you measure the rope to have a length of 1.35 and a mass of 3.38 grams. Assume that the ends of the rope are held fixed and that there is both this traveling wave and the reflected wave traveling in the opposite direction. 1.What is the wavefunction for the standing wave that is produced? 2. In which harmonic is the standing wave oscillating? 3. What is the frequency of the fundamental oscillation?

Explanation / Answer

Comparing the above equation with the general formgiven in class, D(x, t) = A sin(kx ? ?t + ?), one sees that the amplitude is A = 2.33 mm. the frequency is given by f =? / 2? = 742 rad/s / 2? = 118 Hz The wavelength is given by ? =2? / k = 2? / 6.98 rad/m= 0.90 m. The wave travels in the ?x direction since the argumenthas the form of kx + ?t

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