87. (a) From the frequency information, we find ω = 2 π f = 10 π rad/s. A point on the rope undergoing simple harmonic motion (discussed in Chapter 15) has maximum speed as it passes through its "middle" point, which is equal to y m ω . Thus, 5.0 m/s = y m¡ y m = 0.16 m . (b) Because of the oscillation being in the fundamental mode (as illustrated in Fig. 16-23(a) in the textbook), we have λ = 2 L = 4.0 m. Therefore, the speed of waves along the rope is v = f λ = 20 m/s. Then, with μ = m / L = 0.60 kg/m, Eq. 16-26 leads to v = τ μ ¡ τ = v 2 = 240 N 2 2.4 10 N
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This note was uploaded on 04/16/2011 for the course PHYSICS 191262 taught by Professor Najafzadeh during the Spring '09 term at The Petroleum Institute.