# Sinusoidal wave function of t and x

• B
• Ennio
In summary, the conversation discusses characterizing a sinusoidal wave in terms of time and movement along the x direction. The amplitude, angular velocity, and frequency of the wave are all linked together, with the wave number and movement along x also being related. The conversation also mentions describing the disturbance from equilibrium for a single particle in a medium, as well as the shape of a string made up of particles at a certain time or as time evolves.
Ennio
TL;DR Summary
Starting from the domain of t, is it possible to express the sinef function under the domain of movement?
Greetings,

is it possible to characterize a sinusoidal wave in the domain of time and then pass into the domain of movement along x direction?
I start with: a is the amplitude of the sine function and ω is the angular velocity. t is the time. I can express the angular velocity in funct. of the frequency n. In turn, n is velocity of the wave valong x divided its wavelength. Now, 2 pi over lambda is the wave number k and vt is the movement along x.
Does my derivation make sense to you?

E.

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Are you trying to describe the disturbance ##y## from equilibrium
• for a single particle located at ##x=X_P## in a medium as time evolves? ##y(X_P,t)##
• for the shape of a string (made up of a string of particles) at a certain time ##T_0## ? ##y(x,t=T_0)##
• for the shape of a string (made up of a string of particles) as time evolves? ##y(x,t)##

robphy said:
Are you trying to describe the disturbance ##y## from equilibrium
• for a single particle located at ##x=X_P## in a medium as time evolves? ##y(X_P,t)##
• for the shape of a string (made up of a string of particles) at a certain time ##T_0## ? ##y(x,t=T_0)##
• for the shape of a string (made up of a string of particles) as time evolves? ##y(x,t)##
not exactly a disturbance from equilibrium but rather the description of the sine wave evolution i nthe two domains.

## 1. What is a sinusoidal wave function?

A sinusoidal wave function is a mathematical representation of a wave that oscillates back and forth in a regular pattern. It is characterized by a sine or cosine function and can be used to describe various physical phenomena such as sound, light, and electromagnetic waves.

## 2. How is the sinusoidal wave function related to time and position?

The sinusoidal wave function is a function of both time (t) and position (x). It describes the behavior of a wave at a specific point in space and time. As time passes, the wave function changes, and as the wave travels through space, the function changes at different positions along its path.

## 3. What is the equation for a sinusoidal wave function of t and x?

The equation for a sinusoidal wave function of t and x is given by y = A sin(kx - ωt + φ), where A is the amplitude, k is the wave number, ω is the angular frequency, and φ is the phase shift. This equation can be used to calculate the value of the wave function at any time and position.

## 4. How does the amplitude affect the sinusoidal wave function?

The amplitude (A) of a sinusoidal wave function determines the maximum displacement of the wave from its equilibrium position. A larger amplitude means a more pronounced wave, while a smaller amplitude means a less pronounced wave. Amplitude does not affect the frequency or wavelength of the wave, only its intensity.

## 5. How do changes in frequency and wavelength affect the sinusoidal wave function?

The frequency (f) and wavelength (λ) of a sinusoidal wave function are inversely proportional. This means that as the frequency increases, the wavelength decreases, and vice versa. Changes in frequency and wavelength affect the shape and speed of the wave, but not its amplitude or phase.

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