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(μs)
coefficient of kinetic friction(μk)
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:


    

        

            
Name
            
Standard Symbol
            
Field of application
        
        

            
Abbe number
            
V
            
optics (dispersion in optical materials)
        
        

            
Albedo
            
α
            
climatology, astronomy (reflectivity of surfaces or bodies)
        
        

            
Archimedes number
            
Ar
            
motion of fluids due to density differences
        
        

            
Atomic weight
            
M
            
chemistry
        
        

            
Bagnold number
            
Ba
            
flow of bulk solids such as grain and sand. [5]
        
        

            
Biot number
            
Bi
            
surface vs. volume conductivity of solids
        
        

            
Bodenstein number
            
 
            
residence-time distribution
        
        

            
Bond number
            
Bo
            
capillary action driven by buoyancy [6]
        
        

            
Brinkman number
            
Br
            
heat transfer by conduction from the wall to a viscous fluid
        
        

            
Brownell Katz number
            
 
            
combination of capillary number and Bond number
        
        

            
Capillary number
            
Ca
            
fluid flow influenced by surface tension
        
        

            
Coefficient of static friction
            
μs
            
friction of solid bodies at rest
        
        

            
Coefficient of kinetic friction
            
μk
            
friction of solid bodies in translational motion
        
        

            
Colburn j factor
            
 
            
dimensionless heat transfer coefficient
        
        

            
Courant-Friedrich-Levy number
            
ν
            
numerical solutions of hyperbolic PDEs [7]
        
        

            
Damkohler number
            
Da
            
reaction time scales vs. transport phenomena
        
        

            
Darcy friction factor
            
Cf or f
            
fluid flow
        
        

            
Dean number
            
D
            
vortices in curved ducts
        
        

            
Deborah number
            
De
            
rheology of viscoelastic fluids
        
        

            
Decibel
            
dB
            
ratio of two intensities of sound
        
    


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