Question

What will be the position of the oscillator which has the same phase at the same instant of time?
\[\begin{align}
  & Equation=x\left( t \right)=0.00327\sin \left( 72.1x-2.72t \right) \\
 & w=10.433\dfrac{m}{s} \\
\end{align}\]

Answer 1

Hint: Phase difference is used for finding difference in degrees or radians .Something which vibrates is something which oscillates. This question is related to the concept of oscillation and simple harmonic motion. In this question we use the formula of wave speed which is defined as frequency times of wavelength.

Complete answer:
Oscillation is the movement in the fixed interval of time at a periodic motion whose end and start position is fixed. For Example spring, fan, double pendulum, playground swing, string instrument, quantum harmonic oscillator, vibrating string etc. Wave waves are also in periodic motion like water waves, sound waves, and light waves. We can define wave speed as frequency times of wavelength.
\[f=\dfrac{v}{\lambda }\]
Here \[f\] is frequency, \[v\] is speed and \[\lambda \] is wavelength.
SI unit of \[v:\left( \dfrac{m}{s} \right)\]
SI unit of \[\lambda :\left( m \right)\]
SI unit of \[f:\left( Hz \right)\]
There are different types of waves which have different types of oscillation such as longitudinal waves and transverse waves. Oscillation which is parallel to the direction of a wave is called a longitudinal wave. Examples are sound waves, spring waves etc. And Oscillation which is perpendicular to the wave is called transverse wave. Example is light. When overlapping waves occur then that phenomenon is called interference.
Simple harmonic motion is a sinusoidal wave .It is a wave in which a particle moves around a fixed point or straight line with acceleration. Types of simple harmonic motion are damped simple harmonic motion which arises due to friction, forced simple harmonic motion, periodic and oscillatory motion. The two waveforms also have a lagging phase difference . Lagging refers to the relationship between two sinusoidal waveforms of the same frequency.
\[\begin{align}
  & v=\left( \dfrac{\text{coefficient of y}}{\text{coefficient of x}} \right) \\
 & v=\dfrac{2.72}{72.1} \\
\end{align}\]
From the above equation we know that:
\[f=\dfrac{v}{\lambda }\]
On simplifying above equation we get:
\[\lambda =\dfrac{v}{f}.....\] Equation (1)
Where \[f=\dfrac{2\pi }{w}\]
\[w=2.72\]
Putting the values in equation (1) and solving we get:
\[\lambda =\dfrac{{{\left( 2.72 \right)}^{2}}}{72.1\times 2\times \pi }\]
Here we take \[\pi =3.14\]
\[\lambda =\dfrac{7.3984}{452.788}\]
Hence we get the value as:
\[\lambda =0.01633m\].

Note: Pendulum is a very slow oscillator. Water wave is the movement of water in an up and down direction, also called tides, which occurs in oceans. There are oscillators present in chemicals called chemical oscillators which occur when we combine different chemicals in the right order and make new things.