Question

A transverse sinusoidal wave on a string has a period T= 25.0ms and travels in the negative x direction with a speed of 30.0 m/s. At t = 0 , an element of the string at x = 0 has a transverse position of 2.00cm and is traveling downward with a speed of 2.0 m/s .(a) What is the amplitude of the wave?

Answer 1

The amplitude of the wave is 0.022m

How to solve solve for the amplitude

Given data

period T= 25.0ms = 0.025s

speed of 30.0 m/s

t = 0

x = 0

transverse position of 2.00cm = 0.02m

wave equation is = y ( x ) = A cos ( ωx + ∅ )

since:

t = 0

x = 0

0.02 = A cos ( 0 + ∅ )

0.02 = A cos ( ∅ )

speed = v ( x )= 2.0 m/s = d y ( x ) / d x

- 2 = - Aω sin ( ∅ )

dividing the equations as below gives

- Aω sin ( ∅ ) / A cos ( ∅ )

- ω tan ( ∅ ) = - 2 / 0.02

ω tan ( ∅ ) = 100

ω = 2 * pi * f = 2 * pi / T = 2 * pi / 0.025 = 80 * pi

tan ( ∅ ) = 100 /( 80* pi )

tan ( ∅ ) = 0.398

∅ = 0.3787 rad

Amplitude = 0.3787 / cos ∅

Amplitude = 0.022m

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