In a laboratory experiment, two continuous sinusoidal transverse waves are generated on identical stretched strings under equal tension. Wave 1 has frequency \(f_0\) and amplitude \(A_0\). Wave 2 is generated such that its frequency is \(3f_0\) and its amplitude is \(2A_0\). The average power \(P\) transmitted by a mechanical wave on a string is proportional to the square of its frequency and the square of its amplitude (\(P \propto f^2 A^2\)). What is the ratio \(\dfrac{P_2}{P_1}\) of the average power transmitted by Wave 2 to that transmitted by Wave 1?