Standing waves on a wire are described by y{(x, t) = (A_sw sin k x)sin omega t w

Question

Standing waves on a wire are described by y{(x, t) = (A_sw sin k x)sin omega t with A_SW =2 60 mm omega = 986 rad/s . and k = 0 710 pi rad/m The left end of the wire is at x = 0. At what distances from the left end are the nodes of the standng wave x_node = 0.704 + (1.41 m)n, n = 0, 1, 2... x_node = (1.41 m)n, n = 0, 1, 2,... At what distances from the left end are the antinodes of the standing wave? x_antinode = 1.41 m + (1.41m)n, n = 0, 1, 2,... x_antinode = 0.704 cm + (1.41 cm)n, n = 0, 1, 2..x_antinode = 0.704m + (1.41 m)n, n = 0, 1, 2.. x_antinode = 0.704m + (0.704 m)n, n = 0, 1, 2,..

Explanation / Answer

PART A)

y = 0 at nodes

for nodes, sin kx =0

kx = n pi

x = n pi/k = n pi/[0.71 pi]

    = 1.41 n   meter where n=0,1,2....

second option is correct

part B) At antinodes, y will be maximum, i.e. sin kx will be +1 or -1

for nodes, sin kx = +1 or -1

kx =pi (2n+1)/2

x = [ pi (2n+1)/2 ]/[0.71pi]

x =1.41 [(2n+1)/2 ] = 1.41 [n+0.5 ]

= 0.704 + 1.41n    meter

third option is correct

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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