Write names of four dimensionless quantities. If y = A sin(wt - kx) then find out dimension of w/k.

The dimensionless quantities are

Coefficient of static friction(μ_s)

coefficient of kinetic friction(μ_k)

Decibels(dB)

Poissons ratio

Stokes number

for Sin X , X should be dimensionless

here wt-kx should be dimensionless , so dimension of w/k is equal to dimension of x/t which is m/sec or LT^-1

since the argument of any trignometric quantity have to be neccessarily a radian hence it implies dimention of wt-kx has to be the dimention of radian that is dimentionless.hence dimention of w is T^-1and dimention of k is L^-1 hence dimention of w/k is L¹T ^-1.

Hi

There are infinitely many dimensionless quantities and they are often called numbers. very few of them has been listed below:

y = A sin (wt-kx)
According to dimensional analysis , in any term sin ø, ø should be dimensionless
Hence, the term wt-kx is also dimensionless
 where t= time (sec)
            x= distance (m)

for the term to be dimensionless, wt has no units
      units of  w = s^(-1)
                    k = m^(-1)

Now, units of w/k = m/s