Question

The speed of a wave in deep water depends on its wavelength L and the

acceleration of free fall g.

What is a possible equation for the speed v of the wave?

A. v = √(gL/2π)

B. v = gL/4π2

C. v = 2π√(g/L)

D. v =2πg/L

Answer 1

The units on the left-side of the equation should equals the units on the right-side of the equation.

As we can see, the answer A) satisfies this condition:

$$\dfrac{m}{s}=\sqrt{\dfrac{\dfrac{m}{s}\cdot m}{2\pi}},$$ $$\dfrac{m}{s}=\dfrac{1}{2\pi}\cdot \dfrac{m}{s},$$ $$\dfrac{m}{s}= \dfrac{m}{s}.$$

Thus, the answer is A.

Answer:

A) $v=\sqrt{\dfrac{gL}{2\pi}}$