A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x, t) = 2.30 mm cos[(6.98 rad/m)x + (742 rad/s)t]. Being more practical, you measure the rope to have a length of 1.35 m and a mass of 0.00338 kg. You are then asked to determine the following: (a) amplitude; (b) frequency; (c) wavelength; (d) wave speed; (e) direction the wave is traveling; (f) tension in the rope; (g) average power transmitted by the wave.

Solution 28E Step 1: The wavefunction of a travelling wave on a thin rope is y(x,t) = Acos(kx + wt) y(x,t) = 2.30 mm cos[(6.98 rad/m)x + (742 rad/s)t] Step 2: (a).Amplitude A = 2.30 mm Step 3: (b).Frequency of wave f = w/2 f = 742/2 f = 1165.53 Hz Step 4: (c).Wavelength k = 2/ = 2/k = 2/(6.98 rad/s) = 0.900 m