You are holding one end of an elastic cord that is fastened to a wall 3.0 m away. You begin shaking the end of the cord at 3.5 Hz, creating a continuous sinusoidal wave of wavelength 1.0 m. How much time will pass until a standing wave fills the entire length of string?

1.714 s

Explanation:

The equation of a moving wave,

v = λf ... Equation 1

Where v = velocity of the wave, λ = wave length of the wave, f = frequancy of the wave,

Given: λ = 1.0 m, f = 3.5 Hz.

Substitute into equation 1

v = 1.0 (3.5)

v = 3.5 m/s.

From motion,

velocity = distance/time.

v = d/t

t = d/v ... Equation 2

Where distance of the elastic chord from the wall, t = time taken to travel to the other end.

Given: d = 3.0 m, v = 3.5 m/s

Substitute into equation 2

t = 3.0/3.5

t = 0.857 s.

Note: for the wave to form a standing wave, it has to travel twice.

Thus,

Time taken for standing wave to fill the entire length of the string = 2t

= 2*0.857

1.714 s