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The data table shows how the amplitude of a mechanical wave varies with the energy it carries. Analyze the data to identify the mathematical relationship between amplitude and energy. Use your equation to find the energy if the amplitude is 8 units.
Amplitude
1
2
3
4
energy
2
8
18
32

A.66 units
B. 108 units
C. 128 units
D. 88 units ​

Respuesta :

Perplexed20

Answer:

E∝A²

Energy varies as square of change in amplitude

If amplitude of 1 has energy of 2

Amplitude of 2 (double of 1) = (2x2)=4x2=8  4 times the energy at amplitude of 1.

For 8 units of amplitude change

8x8=64x2= 128  or C:

Explanation:

onyebuchinnaji

When the amplitude of the wave is 8 units, the corresponding energy of the wave is 128 units.

The given parameters;

  • first amplitude, A = 1, corresponding energy = 2
  • second amplitude, A = 2, corresponding energy = 8

The energy of a string at  a given amplitude is calculated as follows;

[tex]E = \frac{1}{2} kA^2\\\\\frac{E}{A^2} = \frac{E_1}{A_1^2}[/tex]

When the amplitude is 8, the energy of the wave is calculated as follows;

[tex]\frac{2}{1^2} = \frac{E_2}{8^2} \\\\E_2 = 2(8^2)\\\\E_2 = 2(64)\\\\E_2 = 128 \ units[/tex]

Thus, when the amplitude of the wave is 8 units, the corresponding energy of the wave is 128 units.

Learn more here:https://brainly.com/question/21981451

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