Final answer:
To find the length of the wave that gives the minimum velocity, differentiate the equation v = K√(L/C) with respect to L and set it equal to zero. The length of the wave that gives the minimum velocity is zero.
Step-by-step explanation:
The velocity of a wave of length L in deep water is given by the equation v = K√(L/C). To find the length of the wave that gives the minimum velocity, we can differentiate the equation with respect to L and set it equal to zero. This will give us the value of L that minimizes the velocity.
Let's solve the equation step by step:
Start with the equation v = K√(L/C).
Differentiate both sides of the equation with respect to L to get dv/dL = (1/2K)√(C/L).
Set dv/dL equal to zero and solve for L. This gives us (1/2K)√(C/L) = 0.
Since K and C are positive constants, we can conclude that L must be equal to zero in order to minimize the velocity.
Therefore, the length of the wave that gives the minimum velocity is zero.