Question

henri draws a wave that has a 4 cm distance between the midpoint and the trough. geri draws a wave that has an 8 cm vertical distance from the trough to the crest. which statement best describes the energy in henri and geris waves? henris wave has a higher amplitude and more energy. henris wave and geris wave have the same amplitude and the same energy. henris wave and geris wave have the same amplitude, but geris has more energy. geris wave has a higher amplitude and more energy.

Explanation:

• Amplitude is the distance from the mid - point to the trough (or crest). For Henri's wave, amplitude \(A_{Henri}=4\space cm\).
• The distance from trough to crest is \(2A\). For Geri's wave, if \(2A_{Geri} = 8\space cm\), then \(A_{Geri}=\frac{8}{2}=4\space cm\).
• The energy of a wave (for mechanical waves in the same medium) is related to the square of the amplitude (\(E\propto A^{2}\)). Since \(A_{Henri} = A_{Geri}\), their waves have the same amplitude and the same energy.

Answer:

Henri's wave and Geri's wave have the same amplitude and the same energy.