An example of a wave that has increased amplitude and frequency but decreased wavelength is a phenomenon known as "blue shift" in the context of electromagnetic waves. Blue shift refers to a shift of the wavelength of light towards the shorter (blue) end of the visible spectrum. It occurs when a light source or wave emitter is moving towards an observer.
When an object emitting light moves towards an observer, the motion compresses the waves in the direction of motion, leading to a decrease in the wavelength. At the same time, due to the Doppler effect, the frequency of the waves increases as perceived by the observer. The combination of a decreased wavelength and an increased frequency results in an overall increase in the energy of the waves.
For example, consider a source of visible light emitting predominantly red light waves. If the source moves towards an observer, the wavelength of the emitted light waves decreases, causing the light to shift towards the blue end of the spectrum. The frequency of the waves increases since the number of wave crests passing a fixed point per unit time has increased. As a result, the amplitude and frequency of the wave increase, while the wavelength decreases.
It's important to note that this example specifically applies to electromagnetic waves, such as light, in the context of relative motion between the source and the observer.