Question

A point on a string undergoes simple harmonic motion as a sinusoidal wave passes. When a sinusoidal wave with speed 24 m/s, wavelength 30 cm, and amplitude of 1.0 cm passes, what is the maximum speed of a point on the string?

Answer 1

Answer:

5.03 m/s

Explanation:

Give

Speed = v = 24m/s

Wavelength = λ = 30cm = 0.3m

Amplitude = A = 1.0cm = 0.01m

The velocity of a point in Simple Harmonic Motion

at any time t is given by the following formula

v = ωA cos ωt

The value is the Maximum when cosωt.

The maximum value of cosωt. is 1.

Hence the maximum velocity is ωA

Velocity of the wave v=n λ

n = v/ λ = 24 /0.3 = 80

ω = 2πn = 2π*80 = 502.86 rad/s

Maximum velocity of the particle is

ωA = 502.86 * 0.01 = 5.03m/s