# Frequency amplitude and wavelength relationship with energy

### Wavelength, Frequency, Amplitude, & Intensity - CHEMISTRY COMMUNITY

Frequency is inversely proportional to wavelength, since speed is fixed. This happens when, for whatever reason, too much energy is put into the What's the relationship between amplitude and wavelength, velocity or frequency, and. The Relationship between Wave Frequency, Period, Wavelength, and Velocity When the cork hits the water, that energy travels through the water in waves. The energy of the wave depends on both the amplitude and the If two mechanical waves have equal amplitudes, but one wave has a frequency equal to . This equation can be used to find the energy over a wavelength.

• 16.4: Energy and Power of a Wave
• Energy Transport and the Amplitude of a Wave

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. 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. This produces a sinusoidal wave in the string, which moves with a wave velocity v.

The wave speed depends on the tension in the string and the linear mass density of the string. The total mechanical energy of the wave is the sum of its kinetic energy and potential energy. Amplitudes associated with changes in bulk properties of arbitrarily small regions of the medium The pressure amplitude is the maximum change in pressure the maximum gauge pressure.

The density amplitude is the maximum change in density. Measuring displacement might as well be impossible. For typical sound waves, the maximum displacement of the molecules in the air is only a hundred or a thousand times larger than the molecules themselves — and what technologies are there for tracking individual molecules anyway?

The velocity and acceleration changes caused by a sound wave are equally hard to measure in the particles that make up the medium. Density fluctuations are minuscule and short lived.

## CHEMISTRY COMMUNITY

The period of a sound wave is typically measured in milliseconds. There are some optical techniques that make it possible to image the intense compressions are rarefactions associated with shock waves in air, but these are not the kinds of sounds we deal with in our everyday lives.

Pressure fluctuations caused by sound waves are much easier to measure. Animals including humans have been doing it for several hundred million years with devices called ears. This creates a disturbance within the medium; this disturbance subsequently travels from coil to coil, transporting energy as it moves.

This energy is transferred from coil to coil until it arrives at the end of the slinky. If you were holding the opposite end of the slinky, then you would feel the energy as it reaches your end. In fact, a high energy pulse would likely do some rather noticeable work upon your hand upon reaching the end of the medium; the last coil of the medium would displace your hand in the same direction of motion of the coil. For the same reasons, a high energy ocean wave can do considerable damage to the rocks and piers along the shoreline when it crashes upon it.

How is the Energy Transported Related to the Amplitude? The amount of energy carried by a wave is related to the amplitude of the wave. A high energy wave is characterized by a high amplitude; a low energy wave is characterized by a low amplitude.

As discussed earlier in Lesson 2the amplitude of a wave refers to the maximum amount of displacement of a particle on the medium from its rest position.

The logic underlying the energy-amplitude relationship is as follows: If a slinky is stretched out in a horizontal direction and a transverse pulse is introduced into the slinky, the first coil is given an initial amount of displacement. The displacement is due to the force applied by the person upon the coil to displace it a given amount from rest.

### HubbleSite - Reference Desk - FAQs

The more work that is done upon the first coil, the more displacement that is given to it. The more displacement that is given to the first coil, the more amplitude that it will have. So in the end, the amplitude of a transverse pulse is related to the energy which that pulse transports through the medium.

Putting a lot of energy into a transverse pulse will not effect the wavelength, the frequency or the speed of the pulse.