A transverse harmonic wave travels on a rope according to the following expressi

Question

A transverse harmonic wave travels on a rope according to the following expression: y(x,t) = 0.13sin(2.3x + 17.2t) The mass density of the rope is ? = 0.138 kg/m. x and y are measured in meters and t in seconds. A= 0.13 F= 2.737 Hz 3) What is the wavelength of the wave? 4) What is the speed of the wave? 5) What is the tension in the rope? 6) At x = 3.8 m and t = 0.48 s, what is the velocity of the rope? (watch your sign) 7) At x = 3.8 m and t = 0.48 s, what is the acceleration of the rope? (watch your sign) 8) What is the average speed of the rope during one complete oscillation of the rope?

Explanation / Answer

y(x,t) = 0.13sin(2.3x + 17.2t) ........ A = 0.13 m k = 2.3; ? = 17.2 rad/s ==> f = 17.2 / (2pi) = 2.737 Hz ...amd mass density ? = m/l = 0.138 kg/m ...........3) ? = 2pi / k = 2pi / 2.3 = 2.732 m ................4) speed of wave = ? / k = 17.2 / 2.732 = 6.30 m/s ( = 2pi m/s) ........................5) speed v = ?(T/ ? ) ==> tension in the rope T = v^2*? = 5.47 N ...........................6) velocity of rope v(x,t) = dy(x,t) /dt = 17.2*0.13 cos (2.3x+17.2t) ......so v(3.8 , 0.48) = 2.236 cos (8.74 + 8.256) = 2.138 m/s ...............7) acceleration a(x,t) = dv(x,t)/dt = -17.2^2 * 0.13 sin(2.3x+17.2t) ....so a(3.8 , 0.48) = -35.4592sin(8.74+8.256) = - 11.24 m/s^2 ........

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.