Problem 11.31 Challenge

กำหนดให้ \(m = 0.100 kg\) และ \(L = 10.0 m\)

จาก \(y(x,t) = (0.200 m)sin(πx - 20πt)\)

เทียบรูปกับสมการ \(y(x,t) = Asin(kx - ωt + φ)\)

a) จะได้ \(A = 0.200 m\)

b) จะได้ \(k = π\)

\(\frac{2\pi}{\lambda}= \pi\)

\(\lambda = 2.00 m \;\blacksquare\)

c) จะได้ \(ω = 20π\)

\(2\pi f = 20\pi\)

\(f = 10.0 Hz \;\blacksquare\)

d) จะได้ \(v = fλ = 20.0 m/s \;\blacksquare\)

e) จาก \(v = \sqrt{\frac{T}{\mu}}\)

\(T = \mu v^{2}\)

\(T = (\frac{m}{L})v^{2} = 4.00 N \;\blacksquare\)

f)จาก\(\wp =\frac{1}{2}\mu \omega ^{2}A^{2}v\)

\(\wp =\frac{1}{2}(\frac{m}{L})(2\pi f)^{2}A^{2}v = 15.8 W \;\blacksquare\)

g) จาก \(\wp = \frac{E}{T}\)

\(E = \wp T =\frac{\wp}{f}= 1.58 J \;\blacksquare\)