Question

question 20 of 25
analyze the data to identify the mathematical relationship between the amplitude and energy of a mechanical wave. if mechanical wave a has an amplitude of 1 cm and mechanical wave b has an amplitude of 2 cm, what will be the relationship between the energy carried by the two waves?

a. the amount of energy in wave a is half the amount of energy in wave b.
b. the amount of energy in wave b is four times the amount of energy in wave a.
c. the amount of energy in wave b is half the amount of energy in wave a.
d. the amount of energy in wave a is four times the amount of energy in wave b.

Explanation:

Step1: Analyze the relationship between amplitude and energy

From the table, when amplitude \(A_1 = 1\) unit, energy \(E_1=2\) units; when amplitude \(A_2 = 2\) units, energy \(E_2 = 8\) units. We can observe that \(E=2A^{2}\) (where \(E\) is energy and \(A\) is amplitude).

Step2: Calculate energy for wave A and wave B

For wave A with \(A_A=1\) cm, \(E_A = 2\times(1)^{2}=2\) units. For wave B with \(A_B = 2\) cm, \(E_B=2\times(2)^{2}=8\) units.

Step3: Find the ratio of \(E_B\) to \(E_A\)

\(\frac{E_B}{E_A}=\frac{8}{2} = 4\)

Answer:

B. The amount of energy in wave B is four times the amount of energy in wave A.