Question

The intensity of a wave is
a. Proportional to square of the frequency
b. Proportional to the velocity of wave
c. Proportional to the density of the medium
d. Proportional to the square of the distance of the source from the observer

A. Only d is true
B. a and b are true
C. a, b and c are true
D. a, b, c and d are true

Answer 1

Hint:Here, in this question, we need to show the relationship of the intensity of the wave with respect to the four given options. For this, we will first write the formula of the intensity of the wave and check for the correct given options.

Formula Used:
Mathematically, \[{\text{Intensity}} = \dfrac{{{\text{Power}}}}{{{\text{Area}}}}\]
The square of the wave's amplitude determines the wave's intensity.

The formula of the wave’s intensity is,
\[I = 2{\pi ^2}\mu v{A^2}{\nu ^2}\]
Where, \[\mu \] is the density of the medium in which the wave is travelling, \[v\] is the velocity of the wave, \[A\] is the Amplitude of the wave and \[\nu \] is the frequency of the wave.

Complete step by step solution:
A disturbance in the medium causing the energy to be transported from one place to other without the actual movement of the particles is known as wave. Examples include elastic deformation, pressure changes, electric or magnetic intensity, electric potential, and temperature.

The rate at which a wave transfers energy divided by the region across which the energy is disseminated is described as the wave's intensity (I). In other words, intensity refers to the rate at which energy is transferred per unit of area.The power provided per unit area is denoted as wave intensity.

Now, going through the given options one-by-one-
a. Proportional to square of the frequency.
It is true as, \[I \propto {\nu ^2}\].

b. Proportional to the velocity of the wave.
It is true as, \[I \propto v\]

c. Proportional to the density of the medium.
It is true as, \[I \propto \mu \]

d. Proportional to the square of the distance of the source from the observer.
It is false.

So, option C is correct answer.

Note: For these types of questions, candidates must be aware of the mathematical formula of the intensity of waves along with the different notations present in it.