The Wave Equation

Question

The equation ℎ = 0.019s^2 "gives the height ℎ (in feet) of the largest ocean waves when the wind speed is s knots. What is the wind speed to generate a 22 ft wave?

Answer 1

This is your typical input output function. In this case, once you input you value for wind speed, then you will get your answer in feet as a result. However, the question becomes, what happens if you only have the value for the height of the wave? You then need to find how to get wind speed from the height of the waves. Using algebra techniques your goal becomes to isolate the wind speed, aka s. For this problem I'd refer to reverse PEMDAS as my easiest way to isolate s in steps. It becomes SADMEP(Subtraction, Addition, Division, Multiplication, Exponents, and Parenthesis).

Since there is no subtraction or addition that needs to be moved, then the first two steps are done.

Second step, there is a multiplication that needs to be isolated from s. So to get remove the 0.019 from s, I need to divide 0.019 from both sides. The new equation becomes h/0.019=s². Since no more multiplication or division is attached to the s, then the second step is done

Now going to E, exponents. There is an exponent attached to the s. So to continue isolating s, I need to remove the exponent. To remove the squared I need to do the exact opposite by square rooting both sides. The new equation becomes √(h/0.019) = s

Now you can start solving to find the wind speed since s is fully isolated. Plug in the numbers and solve. √(22/0.019) = √1157 = 34 = s

So s = 34, which means that it takes a wind speed of 34 knots to generate a 22 feet wave.