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

Answer:

t₁ - t₂ = 0.0011 s

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 = $\dfrac{\pi}{180}sin^{-1}(\dfrac{1}{3})$......(1)

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

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

subtracting both the equation (1)-(2)

600(t₁-t₂) =  $\dfrac{2\pi}{180}sin^{-1}(\dfrac{1}{3})$

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