Atransverse sinusoidal wave on a string is moving in the −x-direction. its speed is 30.0 m/s, and its period is 16.0 ms. at t = 0, a colored mark on the string at x = 0 has a vertical position of 2.00 cm and is moving down with a speed of 1.50 m/s.(a)
(a) what is the amplitude of the wave?

(b) what is the initial phase angle?

(c) what is the maximum transverse speed of an element of the string?

(d) write the wave equation for the wave.

Explanation:

Speed of wave v = 30 m /s

Time period T = 16 x 10⁻³ s

a )

At x = 0 , y = 2 cm so amplitude A  = 2 cm

b ) At t = 0 , the particle is at the top and going down so

initial phase = π / 2

c ) Maximum transverse speed will be equal to ωA

where ω is angular velocity and A is amplitude

ω = 2π / T

= 2x 3.14 / 16 x 10⁻³

= 392.5 rad / s

A = 2 cm = 2 x 10⁻²

ωA

= 392.5  x 2 x 10⁻²

= 7.85 m/s

d )

wave equation

y = A sin (  ωt + kx + π / 2 )

y = 2 x 10⁻² cos ( 392.5 t + kx )

velocity = ω / k

k = ω / v

= 392.5  / 1.5

= 261.67

wave equation

y = 2 x 10⁻² cos ( 392.5 t + 261.67 x ) in metre.

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explanation:

no. dot product   =0 when vecs at right angles