Use the wave equation to find the speed of a wave given by -

y(x,t)=(3.0mm)sin[(4.00m-1)x(7.00s-1)t].

Short Answer

Expert verified

The speed of the wave is 1.75 m/s

Step by step solution

01

The given data

The given equation for the wave,y(x,t)=(3.0mm)sin[(4.00m-1)x(7.00s-1)t]

02

Understanding the concept of the wave equation

The solution of wave equation is given by,

y(x,t)=ymsin(kx-ωt)

By comparing this equation with the given equation, we can calculate the speed of the given wave.

Formula:

The speed of the wave,v=ω/k (i)

03

Calculation of the speed of wave

By comparing the given equation with the solution of the wave equation

y(x,t)=(3.0mm)sin[(4.00m-1)x(7.00s-1)t]

Comparing the given equation with general that is,yx,t=ymsinsinkx-wt we get

We can get, angular frequency,ω=7.00rad/s

Wave number,k=4.00/rad

Using equation (i), we get the speed of the wave as

v=7.00s-14.00m-1=1.75m/s

Hence, the value of the speed of the wave is1.75m/s

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