Question

In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is \[0.17\sec \] then the frequency of wave is
A. $1.47Hz$
B. $0.36Hz$
C. $2.94Hz$
D. $2.48Hz$

Answer 1

Hint: To answer the question, we will first consider the time T, then write the expression for the time it takes for a point to travel from maximum displacement to zero displacement, and since it is already given to us in the question, we will equalise it with the expression and find the value of T.

Complete answer:
Let us consider $T$ be the time period.
As a result, the time it takes for a point to travel from maximum displacement to zero displacement is $ = \dfrac{T}{4}$
Given that time, the time it takes for a point to move from maximum displacement to zero displacement is \[0.170s\]
Therefore, according to the question;
$\dfrac{T}{4} = $ \[0.17\sec \]
Now, we will cross multiply
$ \Rightarrow T = 0.17 \times 4$
$\therefore T = 0.68$
As we all know, frequency; $\left( n \right) = \dfrac{1}{T}$
$
   \Rightarrow n = \dfrac{1}{{0.68}} \\
  \therefore n = 1.47Hz \\
 $
Therefore the frequency of the wave is $1.47Hz$
The correct option is: (A) $1.47Hz$

Note:
In physics, the sine wave is significant because it preserves its wave structure when combined with another sine wave of the same frequency, phase, and magnitude. This characteristic is unique to the periodic waveform. This attribute gives it significance in Fourier analysis and distinguishes it acoustically.