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In case of simple harmonic motion the velocity max at the equilibrium will be a w

Here w (omega) is the angular frequency = 2 pi nu (frequency)

Now kinetic energy E = 1/2 m v^2 = 1/2 * m * a^2 * w^2

Here a is amplitude.

So energy seems proportional to the square of amplitude

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It really depends on the specific situation. In some cases, it is related to the fact that energy is proportional to the fact that kinetic energy is proportional to the square of the speed - at higher amplitudes, the particles will also move at greater speeds.

Q: Where does the relationship Energy is proportional to Amplitude squared come from?

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Yes. Basically, the energy is proportional to the square of the amplitude.Yes. Basically, the energy is proportional to the square of the amplitude.Yes. Basically, the energy is proportional to the square of the amplitude.Yes. Basically, the energy is proportional to the square of the amplitude.

Nope, Energy is directly proportional to square of amplitude. :)

The intensity will increase if the energy increase. The intensity is proportional to the square of the amplitude of a wave.

they are directly proportional.

-- Frequency and wavelength are inversely proportional. Their product is constant, and is the speed of the wave. They're entirely unrelated to amplitude or energy. -- A wave with greater amplitude carries more energy than one with smaller amplitude does. -- IF your wave happens to be an electromagnetic one, THEN the energy carried by each quantum is proportional to the frequency.

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As the amplitude of a wave increases, the energy increases. In general terms the energy transported by a wave is proportional to the amplitude squared.

Yes. Basically, the energy is proportional to the square of the amplitude.Yes. Basically, the energy is proportional to the square of the amplitude.Yes. Basically, the energy is proportional to the square of the amplitude.Yes. Basically, the energy is proportional to the square of the amplitude.

Nope, Energy is directly proportional to square of amplitude. :)

Frequency.

Amplitude squared is the amount of energy in a wave. The simplest calculations would be for a string wave.

no

The intensity will increase if the energy increase. The intensity is proportional to the square of the amplitude of a wave.

they are directly proportional.

They are all measueres of sound waves. Amplitude is the term for the maximum difference in pressures between the peaks and troughs of a sound wave. Intensity is a measure of the energy content of a wave, and is proportional to amplitude squared. The decibel is an anthropic (based on human senses) measure of sound intensity, proportional to the logarithm of intensity.

The energy and the amplitude are related in such a way that, the greater the amplitude the greater is the energy. The sound pressure amplitude tells about how loud the tone will be.

-- Frequency and wavelength are inversely proportional. Their product is constant, and is the speed of the wave. They're entirely unrelated to amplitude or energy. -- A wave with greater amplitude carries more energy than one with smaller amplitude does. -- IF your wave happens to be an electromagnetic one, THEN the energy carried by each quantum is proportional to the frequency.

Temperature is a measure of how much energy an object has. Einstein's famous equation states the relationship your asking about; E=mc2. That is, the amount of energy an object has is proportional to its mass multiplied by the speed of light squared.