Explanation:
(a)  It is known that equation for transverse wave is given as follows.
                  y =  
Now, we will compare above equation with the standard form of transeverse wave equation,
                  y =  
where,    A is the amplitude = 0.09 m
               k is the wave vector =  
                is the angular frequency =
 is the angular frequency =  
               x is displacement = 1.40 m
               t is the time = 0.16 s
Now, we will differentiate the equation with respect to t as follows.
The speed of the wave  will be:
                    v(t) =  
                 v(t) =  
         v(t) =  
           v(t) = -0.84 m/s
The acceleration of the particle in the location is
             a(t) =  
            a(t) =  
            a(t) =  
            a(t) = -9.49  
Hence, the value of transverse wave is 0.84 m/s and the value of acceleration is 9.49  .
.
(b)  Wavelength of the wave is given as follows.
                 
               
                = 22 m
 = 22 m
The period of the wave is
              T =  
              T =  
                 = 0.5 sec
Now, we will calculate the speed of propagation of wave as follows.
                     v =  
                        =  
                        = 44 m/s
therefore, we can conclude that wavelength is 22 m, period is 0.5 sec, and speed of propagation of wave is 44 m/s.