# Relationship between amplitude and rate of energy transfer

### Acoustics Chapter One: What is Amplitude? | page 3

Explain how the energy and amplitude of an electromagnetic wave are related. frequency of water molecules), the transfer of energy is much more efficient. where c is the speed of light, ε0 is the permittivity of free space, and E0 is the be expressed in terms of the magnetic field strength by using the relationship B= Ec. 1 watt = 1 newton (N) of work or energy transferred per second* As the surface area of the sound sphere expands, the amount of energy generated by the sound A few more relationships between amplitude, intensity and power: intensity is. The Relationship between Wave Frequency, Period, Wavelength, and Velocity amplitude and the period of waves are affected by the transfer of energy from a.

• Introduction to Computer Music: Volume One

In this section, we examine the quantitative expression of energy in waves. This will be of fundamental importance in later discussions of waves, from sound to light to quantum mechanics. Energy in Waves The amount of energy in a wave is related to its amplitude and its frequency. Large-amplitude earthquakes produce large ground displacements.

Loud sounds have high-pressure amplitudes and come from larger-amplitude source vibrations than soft sounds. Large ocean breakers churn up the shore more than small ones.

Consider the example of the seagull and the water wave earlier in the chapter Figure Work is done on the seagull by the wave as the seagull is moved up, changing its potential energy. The larger the amplitude, the higher the seagull is lifted by the wave and the larger the change in potential energy. The energy of the wave depends on both the amplitude and the frequency.

If the energy of each wavelength is considered to be a discrete packet of energy, a high-frequency wave will deliver more of these packets per unit time than a low-frequency wave. We will see that the average rate of energy transfer in mechanical waves is proportional to both the square of the amplitude and the square of the frequency. If two mechanical waves have equal amplitudes, but one wave has a frequency equal to twice the frequency of the other, the higher-frequency wave will have a rate of energy transfer a factor of four times as great as the rate of energy transfer of the lower-frequency wave.

It should be noted that although the rate of energy transport is proportional to both the square of the amplitude and square of the frequency in mechanical waves, the rate of energy transfer in electromagnetic waves is proportional to the square of the amplitude, but independent of the frequency.

### Energy Transport and the Amplitude of a Wave

Power in Waves Consider a sinusoidal wave on a string that is produced by a string vibrator, as shown in Figure The string vibrator is a device that vibrates a rod up and down. A string of uniform linear mass density is attached to the rod, and the rod oscillates the string, producing a sinusoidal wave.

The rod does work on the string, producing energy that propagates along the string.

As the energy propagates along the string, each mass element of the string is driven up and down at the same frequency as the wave. Each mass element of the string can be modeled as a simple harmonic oscillator.

A string vibrator is a device that vibrates a rod. A string is attached to the rod, and the rod does work on the string, driving the string up and down. When done by a neuronal circuit like the circuits in your brain that connect to your ears the resulting sensation is called loudness. The intensity of a sound wave is a combination of its rate and density of energy transfer. It is an objective quantity associated with a wave.

Loudness is a perceptual response to the physical property of intensity. It is a subjective quality associated with a wave and is a bit more complex. As a general rule the larger the amplitude, the greater the intensity, the louder the sound. Sound waves with large amplitudes are said to be "loud". Sound waves with small amplitudes are said to be "quiet" or "soft".

The word "low" is sometimes also used to mean quiet, but this should be avoided.

## Energy Transport and the Amplitude of a Wave

Use "low" to describe sounds that are low in frequency. Consider two identical slinkies into which a pulse is introduced. If the same amount of energy is introduced into each slinky, then each pulse will have the same amplitude.

But what if the slinkies are different?

### Intensity – The Physics Hypertextbook

What if one is made of zinc and the other is made of copper? Will the amplitudes now be the same or different?

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If a pulse is introduced into two different slinkies by imparting the same amount of energy, then the amplitudes of the pulses will not necessarily be the same. In a situation such as this, the actual amplitude assumed by the pulse is dependent upon two types of factors: Two different materials have different mass densities.

The imparting of energy to the first coil of a slinky is done by the application of a force to this coil.

## 16.4: Energy and Power of a Wave

More massive slinkies have a greater inertia and thus tend to resist the force; this increased resistance by the greater mass tends to cause a reduction in the amplitude of the pulse. Different materials also have differing degrees of springiness or elasticity.

A more elastic medium will tend to offer less resistance to the force and allow a greater amplitude pulse to travel through it; being less rigid and therefore more elasticthe same force causes a greater amplitude.

Energy-Amplitude Mathematical Relationship The energy transported by a wave is directly proportional to the square of the amplitude of the wave. This energy-amplitude relationship is sometimes expressed in the following manner.

This means that a doubling of the amplitude of a wave is indicative of a quadrupling of the energy transported by the wave. A tripling of the amplitude of a wave is indicative of a nine-fold increase in the amount of energy transported by the wave.