Sketch a sinusoidal wave with an amplitude of 2 cm and a wavelength of 6 cm. This wave represe

step 1 Amplitude is 2 centimeter so that's a wave with amplitude 2 centimeter where this much is 1 cent

Sketch a sinusoidal wave with an amplitude of 2 cm and a...

Sketch a sinusoidal wave with an amplitude of $2 \mathrm{~cm}$ and a wavelength of $6 \mathrm{~cm}$. This wave represents the electric field portion of a visible EM wave traveling to the right with intensity $I_{0}$. (a) Sketch an identical wave beneath the first. What is the amplitude (in $\mathrm{cm}$ ) of the sum of these waves? (b) What is the intensity of the new wave? (c) Sketch two more coherent waves beneath the others, one of amplitude $3 \mathrm{~cm}$ and one of amplitude $1 \mathrm{~cm}$, so all four are in phase. What is the amplitude of the four waves added together? (d) What intensity results from adding the four waves?

Sketch a sinusoidal wave with an amplitude of $2 \mathrm{~cm}$ and a wavelength of $6 \mathrm{~cm}$. This wave represents the electric field portion of a visible EM wave traveling to the right with intensity $I_{0}$. (a) Sketch an identical wave beneath the first. What is the amplitude (in $\mathrm{cm}$ ) of the sum of these waves?
(b) What is the intensity of the new wave?
(c) Sketch two more coherent waves beneath the others, one of amplitude $3 \mathrm{~cm}$ and one of amplitude $1 \mathrm{~cm}$, so all four are in phase. What is the amplitude of the four waves added together?
(d) What intensity results from adding the four waves?

Key Concepts

Sinusoidal Waves

A sinusoidal wave is a smooth, repetitive oscillation characterized by its amplitude, wavelength, and frequency. The amplitude determines the maximum displacement from the equilibrium position, while the wavelength is the distance over which the wave's shape repeats. This concept is fundamental in describing many physical phenomena, such as sounds and light, where the wave’s form defines its energy and transmission properties.

Wave Superposition

The superposition principle states that when two or more waves overlap in space, the resultant displacement at any given point is the algebraic sum of the displacements of the individual waves. This principle is crucial in understanding how waves interact, as seen in interference effects, where waves add constructively or destructively depending on their relative phases.

Coherent Waves and Constructive Interference

Coherent waves are waves that maintain a constant phase relationship, meaning their peaks and troughs align consistently. When coherent waves are in phase, they interfere constructively, leading to a resultant wave with an amplitude that is the sum of the individual amplitudes. This is important in applications where enhancing the wave's amplitude and therefore its energy is desired.

Intensity-Amplitude Relationship

The intensity of a wave, which is a measure of its energy transport per unit area, is proportional to the square of its amplitude. This quadratic relationship means that if the amplitude of a wave is doubled, its intensity increases by a factor of four. Understanding this relationship is key in fields such as optics and acoustics, where the energy of the waves plays a critical role in system responses and energy transfer.

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