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) = 0.17sin(2.6x + 17.2t). The mass density of the rope is = 0.104 kg/m. x and y are measured in meters and t in seconds.

2.) What is the frequency of oscillation of the wave?

3.) What is the wavelength of the wave?

6) At x = 3.4 m and t = 0.47 s, what is the velocity of the rope? (watch your sign)

7.) At x = 3.4 m and t = 0.47 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

2) frequency = w / 2 pi = 17.2 / 2 pi

frequency = 2.74 Hz

3) wavelength lambda = 2 pi / k = 2 pi / 2.6

lambda = 2.42 m

6) y = 0.17 sin (2.6x + 17.2t)

vy = dy / dt = 2.924 * cos (2.6x + 17.2 t)

x = 3.4 m and t = 0.47 s

= 2.924 * cos (2.6*3.4 + 17.2*0.47) = 2.924 * cos (16.92 rad) = -1.05 m/s

7) ay = d vy / dt = -2.924 * 17.2 sin (2.6x + 17.2 t)

x = 3.4 m and t = 0.47 s

= -46.9 m/s2

8) v = 4 A / T = 4 * 0.17 / (1/2.74)

average speed = 1.86 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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