Question

The power versus time for a point on a string (μ = 0.06 kg/m)  in which a sinusoidal traveling wave is induced is shown in the following figure. The wave is modeled with the wave equation y(x, t) = A sin[(25.43 m⁻¹)x − ωt]. What are the frequency (in Hz) and amplitude (in m) of the wave?

The power versus time or a point on a string μ 0.06 kg/m n which a sinusoidal traveling wave sind ce s snow in the ollowing figure. The ave s model with e equation y(x, t) A sint(25.43 m-1x - at]. What are the frequency (in Hz) and amplitude (in m) of the wave? Power (W) 90 80 70 60 50 40 30 20 10 Time (s) 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 (s frequency x Hz amplitude x m

Answer 1

Power : P = F.U-TUCO (90-9)

Power : P = Tusin(8)

For small angles:

$\theta \approx sin\theta$

$P = Tv \theta$

y = Asin(kx-wt)

$v = \frac{\partial y}{\partial t} = -Aw cos(kx - wt)$

Akcos(krwt)

from the given figure:

time period: (peak to peak time)

$f = \frac{1}{T_P} = \frac{1}{0.02} = 50Hz$

Amplitude of power:

also we can write velocity of wave as:

$v = \sqrt{\frac{T}{\mu}}\Rightarrow T = \mu v^2$

$\mu*v^2* A^2 w = 40$

$w = \frac{2\pi}{T_P} = \frac{2\pi}{0.02} = 314.2 rad/s$

amplitude of wave velocity:

Answers:

$f = \frac{1}{T_P} = \frac{1}{0.02} = 50Hz$