# Potential energy in standing wave compared to traveling wave

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• versine
In summary, the unique point in a traveling wave on a string is the element at maximum displacement which has zero instantaneous velocity and minimum tension. This element has the minimum energy compared to other elements along the sinusoidal contour. However, this does not mean that a wavelength of sinusoidally contoured string has less potential energy than a straight string, as the former is longer and has greater elastic potential energy. As the sinusoidal contour moves along the string, it transports energy. This concept also applies to standing waves, where kinetic energy and potential energy are related to a function of position and are both zero at nodes, while the function has a maximum value at antinodes.
versine
TL;DR Summary
Why is the potential energy of a standing wave maximum when the displacement is maximum, but for a traveling wave, it is when the displacement is zero?
From hyperphysics, "The unique point in the case of the traveling wave in the string is the element of the string that is at the maximum displacement as the wave passes. That element has a zero instantaneous velocity perpendicular to the straight string configuration, and as the wave goes "over the hump", it also has minimum tension. So that element of the string has the minimum energy compared to other elements along the sinusoidal contour. This does not imply that a wavelength of the sinusoidally contoured string has less potential energy than the straight string. The sinusoidally contoured string is longer than a wavelength of straight string and will have greater elastic potential energy. As that sinusoidal contour moves along the string, it transports energy. "

Doesn't this also apply to a standing wave since it is a superposition of two traveling waves?

I think for standing waves
kinetic energy + potential energy = f(x) a function depending on the position.
It means when displacement is maximum kinetic energy is zero.
At nodes kinetic energy = potential energy = f(x) = 0. At antinodes f(x) has maximum value.

## 1. What is the difference between potential energy in a standing wave and a traveling wave?

The main difference between potential energy in a standing wave and a traveling wave is the way in which the energy is distributed. In a standing wave, the energy is concentrated in specific locations, known as nodes and antinodes, where the amplitude of the wave is at its maximum or minimum. In a traveling wave, the energy is evenly distributed along the length of the wave.

## 2. How does the potential energy of a standing wave compare to that of a traveling wave?

The potential energy of a standing wave is generally higher than that of a traveling wave. This is because the energy is concentrated in specific locations in a standing wave, while it is spread out in a traveling wave. However, the total amount of potential energy in both types of waves depends on factors such as the amplitude and frequency of the wave.

## 3. Can potential energy be transferred between a standing wave and a traveling wave?

Yes, potential energy can be transferred between a standing wave and a traveling wave. When a standing wave is formed, the energy is initially transferred from the traveling wave that created it. Similarly, when a standing wave is disrupted, the energy is transferred back into a traveling wave.

## 4. How does the amplitude of a wave affect its potential energy?

The amplitude of a wave directly affects its potential energy. The higher the amplitude, the greater the potential energy. This is because the amplitude is a measure of the displacement of the wave from its equilibrium position, and the greater the displacement, the more potential energy is stored in the wave.

## 5. What factors influence the potential energy of a standing wave?

The potential energy of a standing wave is influenced by several factors, including the amplitude, frequency, and tension of the wave. The amplitude affects the amount of potential energy stored in the wave, while the frequency and tension determine the number and location of nodes and antinodes, which also impact the potential energy distribution in the wave.

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