Question

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1. arnold makes a graph of two mechanical waves, which he calls wave a and wave b. he draws wave a with a lighter line and wave b with a darker line.

how can the properties of arnolds two waves best be described?
a. both waves have the same frequency but different wavelengths.
b. both waves have the same amplitude but different wavelengths.
c. both waves have the same frequency but different amounts of energy.
d. both waves have the same amplitude but different amounts of energy.

Explanation:

• Frequency: The number of wave cycles per unit time. Looking at the graph, both waves complete the same number of cycles in the same time interval, so they have the same frequency.
• Amplitude: The maximum displacement from the rest position. Wave A has a smaller amplitude than Wave B.
• Energy of a mechanical wave (for waves in the same medium): Energy is related to amplitude (\(E\propto A^{2}\), where \(E\) is energy and \(A\) is amplitude). Since amplitudes are different, energies are different.

Answer:

C. Both waves have the same frequency but different amounts of energy.