Question

If a wave y(x, t) (6.0 mm) sin(kx (600 rad/s)t f) travels along a string, how much time does any given point on the string take to move between displacements y 2.0 mm and y 2.0 mm?

Answer 1

t₁ - t₂ = 0.0011 s

Step-by-step explanation:

given,

y(x, t) = (6.0 mm) sin( kx + (600 rad/s)t + Φ)

now,

y m = 6 mm ω = 600 rad/s

y₁ = + 2.0 mm y₂ = -2 .0 mm

now,

2 = (6.0 mm) sin( kx + (600 rad/s)t + Φ)

-2 = (6.0 mm) sin( kx + (600 rad/s)t + Φ)

so,

kx + (600 rad/s)t₁ + Φ =
`(\pi)/(180)sin^(-1)((1)/(3))`......(1)

we have multiplied with π/180 to convert angle into radians

kx + (600 rad/s)t₂ + Φ =
`(\pi)/(180)sin^(-1)(-(1)/(3))`......(2)

subtracting both the equation (1)-(2)

600(t₁-t₂) =
`(2\pi)/(180)sin^(-1)((1)/(3))`

now,

t₁ - t₂ = 0.0011 s

time does any given point on the string take to move between displacements is equal to 0.0011 s