Question

A travelling wave is given by the equation y= 2 sin (0.5t + 0.3), what is the initial phase of the wave
A. 0.3
B. 0.8
C. 0.5
D. 0

Answer 1

Hint: In order to solve this numerical, we should compare the given equation with the wave equation. Also we should understand how to find the angular velocity and the phase of the particle.

Complete step by step answer:
The phase of a vibrating particle at any instant is the state of the vibrating (or) oscillating particle regarding its displacement and direction of vibration at that particular instant.
By using the expression, the position of a particle with respect to the function of time is given by
Y = A sin (ωt + Φ)
Where (ωt + Φ) is the phase of the particle, the phase angle at time t = 0 is known as the initial phase.
From the conditions, by putting time = 0.
Hence, the initial phase = 0.3

The initial phase of the wave is obtained Hence the correct answer is (A).

Additional information: The phase of the periodic function F be the variable of time t which represents the number of periods swept by the variable. The symbol which is denoted by Φ(t) and it varies one full complete cycle. It can be measured in angular units such as in radians or in degrees.

Note:The two particles executing the simple harmonic motion with respect to the mean position when there is a difference in total phase angle exhibits which is commonly called the phase difference. Also when the two particles vibrate in the same phase, then its phase difference between them is an even multiple of π.