Question

Figure shows a snapshot for a travelling sine wave along a string. Four elemental portions a,b,c and d are indicated on the string. The elemental portion which has maximum potential energy is/are

Answer 1

Hint : A wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities in physics, mathematics, and related fields, often represented by a wave equation. At least two field concentrations in the wave medium are present in physical waves. Periodic waves occur as quantities oscillate continuously around an equilibrium (resting) value at a certain frequency.

Formula used:
${u_p} = \dfrac{1}{2} \times p \times {v^2} \times {\left( {\dfrac{{\partial y}}{{\partial x}}} \right)^2}$
${u_p}$ = potential energy
P = momentum
V= velocity
$\left( {\dfrac{{\partial y}}{{\partial x}}} \right) = $slope


Complete step-by-step solution:
Potential energy is the energy that an object holds due to its location in relation to other objects, internal pressures, electric charge, or other causes.
The gravitational potential energy of an object, which is determined by its density and distance from another object's centre of mass, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field are all examples of potential energy. The joule, denoted by the letter J in the International System of Units (SI), is the SI's energy unit.
 We know that the potential energy at volume is
${u_p} = \dfrac{1}{2} \times p \times {v^2} \times {\left( {\dfrac{{\partial y}}{{\partial x}}} \right)^2}$
We know that the potential energy is proportional to the square of the slope of the wave graph.
$m = \dfrac{{dy}}{{dx}}$
The slope is maximum here at point a, m = $\infty $
Hence at point a the potential energy is maximum.

Note: Since the role of possible forces working on a body moving from a start to an end position is determined solely by these two positions and not by the body's direction, a feature known as potential can be measured at these two positions to assess this work.