A sinusoidal transverse wave is traveling along a string in the negative directi

Question

A sinusoidal transverse wave is traveling along a string in the negative direction of an x axis. The figure shows a plot of the displacement as a function of position at time t = 0; the y intercept is 4.0 cm. The string tension is 3.4 N, and its linear density is 44 g/m. Find the (a) amplitude, (b) wavelength, (c) wave speed, and (d) period of the wave. (e) Find the maximum transverse speed of a particle in the string.If the wave is of the form
y(x,t) = ym sin(kx - t + ),
what are (f) k, (g) , and (h) , and (i) the correct choice of sign in front of ?

Explanation / Answer

(a) from figure amplitude is 5 cm

(b) from figure wavelength is 40 cm

(c) V = (T/u)^0.5

v = (3.4/0.044)^0.5

v = 8.79 m/s

(d) v = lamda/T

8.79 = 0.4/T

T = 0.0455 s

(e) Vmax = Aw = A*2pi/T

= 0.05*2*3.14/0.0455

Vamx = 6.9 m/s

(f) k = 2pi/lamda = 2*3.14/0.4

k = 15.7 rad/m

(g) w = 2pi/T = 2*3.14/0.0455

w = 138 rad/s

(h) y = ym*sin(kx-wt+)

4 = 5*sin(0-0+)

= 0.927 rad

(I) y(x,t) = ym sin(kx - t + )

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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