The displacement of a particle of a string carrying a traveling wave is given by y = (3.0 cm)sin 6.28(0.5x - 50t),

Where x is in cm and t in second. Find the speed of the wave.

Given , y = (3.0 cm)sin 6.28(0.5x - 50t),

Comparing with the standard wave equation y = A sin(kx - ωt) = Asin2π$\left(\frac{\mathrm{x}}{\mathrm{\lambda }}-\frac{\mathrm{t}}{\mathrm{T}}\right)$, we get:

Amplitude = 3.0 cm

wavelength = 1/0.5 = 2 cm

and frequency = 1/T = 50 Hz

The speed of the wave can be obtained by, 

v = $\mathit{\nu }\mathit{\lambda }$ 

= 50 x 2 = 100 cm/sec