QuestionJune 12, 2025

Which of the following longitudinal waves has the greatest energy? amplitude=6cm;wavelength=4cm;period=10seconds amplitude=10cm ; wavelength =6 cm; period =4 seconds amplitude=4cm;wavelength=10cm;period=6seconds

Which of the following longitudinal waves has the greatest energy? amplitude=6cm;wavelength=4cm;period=10seconds amplitude=10cm ; wavelength =6 cm; period =4 seconds amplitude=4cm;wavelength=10cm;period=6seconds
Which of the following longitudinal waves has the greatest energy? amplitude=6cm;wavelength=4cm;period=10seconds amplitude=10cm ; wavelength =6 cm; period =4 seconds amplitude=4cm;wavelength=10cm;period=6seconds

Solution
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Answer

The second wave has the greatest energy. Explanation 1. Identify the formula for energy in a wave The energy of a wave is proportional to the square of its amplitude and inversely proportional to its period. Thus, E \propto \frac{A^2}{T}. 2. Calculate energy for each wave For the first wave: E_1 \propto \frac{6^2}{10} = \frac{36}{10} = 3.6. For the second wave: E_2 \propto \frac{10^2}{4} = \frac{100}{4} = 25. For the third wave: E_3 \propto \frac{4^2}{6} = \frac{16}{6} \approx 2.67. 3. Compare energies Compare E_1, E_2, and E_3: 3.6, 25, 2.67.

Explanation

1. Identify the formula for energy in a wave<br /> The energy of a wave is proportional to the square of its amplitude and inversely proportional to its period. Thus, $E \propto \frac{A^2}{T}$.<br />2. Calculate energy for each wave<br /> For the first wave: $E_1 \propto \frac{6^2}{10} = \frac{36}{10} = 3.6$.<br /> For the second wave: $E_2 \propto \frac{10^2}{4} = \frac{100}{4} = 25$.<br /> For the third wave: $E_3 \propto \frac{4^2}{6} = \frac{16}{6} \approx 2.67$.<br />3. Compare energies<br /> Compare $E_1$, $E_2$, and $E_3$: $3.6$, $25$, $2.67$.
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