Question

The wave equation of a wave is y = 5 sin (0.01x - 2t) where x and y are in cm. What is the speed of a wave?

Answer 1

Answer:

The velocity is wt where w is angular velocity than speed is 2

Answer 2

Answer:

velocity of wave,v = 200 cm/s

Explanation:

For any general wave in sinusoidal form  

y=Asin(k.x−ωt+ϕ).....(1)

where,

A= Amplitude

k  = wave number=2πλ

where  λ  is wavelength.

ω=2πf  = angular frequency,

where  f=1/T is frequency, and T is time period.

ϕ  = phase angle shift.

Given,

y = 5 sin (0.01x - 2t).....(2)

by comparing eq(1) and (2), we get

k = 0.01

and ω = 2

=> 2πf = 2

=> f =1/π

Now,

wavelength, λ =$\dfrac{2\pi}{k}$

                        =$\dfrac{2\pi}{0.01}$

                        =628 cm

speed of the wave, v = λ.f

                                    $=628\times \dfrac{1}{\pi}\\\\=200\ cm/s$