Question

Four traveling waves are described by the following equations, where all quantities are measured in SI units and y represents the displacement.

Which of these waves have the same speed?

      I:    y = 0.12 cos(3x - 24t)

      II:  y = 0.15 sin(6x + 32t)

      III: y = 0.13 cos(6x + 24)

      IV: y = -0.27 sin(3x - 42t)

Answer 1

As we know the standard wave equation:

where A= Amplitude

Now compare all four options with standard equation of wave.

to compare them with standard equation, we need to change the cosine equation into the sin equation.

Now to get speed from each equation we need to find frequency and wavelength because

Standard form of wave equation is also   

so in equaton 1.  

and

Hence velocity in equation 1 is v=24*1/3=8m/s

similarly in equation2, which means wave is travelling in negative xdirection

and

so velocity= 32*1/6 =5.333m/s

similarly frequency in equatin3 is -24 and wavelength is 1/6

hence velocity in equation3 is 24*1/6 =4m/s

similarly frequency in equatin4 is 42 and wavelength is 1/3

hence velocity in equation3 is 42*1/3 =14m/s

so speeds in all the equations are different. none of the velocities are same.