Question

When we crack a whip a loud noise is created why ?

Answer 1

Hint: According to conservation of energy, the total energy of an isolated system remains constant; it only changes from one form to another and sound is also a form of energy. Loud noise means a large amount of energy.

Complete step by step answer:
When we crack a whip we transfer the potential energy stored in our body to the whip in form of kinetic energy(KE) which is given by the formula
$K.E.=\dfrac{1}{2}m{{v}^{2}}$
Where $m$ = mass of the moving body and $v$ = velocity of the moving body.

As the energy travels along the whip the mass of the moving part of the whip decreases continuously but according to conservation of energy the total energy remains conserved so accordingly the velocity of the moving part increases continuously. When the whip’s only end part is in motion the mass becomes very less and accordingly the velocity becomes very high which can sometimes reach the velocity of sound and create a sonic boom which is very loud.

Let us take the initial mass of whip be ‘$M$’ and at the end be ‘$m$’ and velocity at the starting be ‘$v$’ and the end be ‘$V$’ than according to the conservation of energy the total energy will be conserved so we can say Kinetic Energy at the starting = Kinetic Energy at the end, mathematically –
$\dfrac{1}{2}M{{v}^{2}}=\dfrac{1}{2}m{{V}^{2}}$
$\therefore V={{(\dfrac{M}{m}{{v}^{2}})}^{\dfrac{1}{2}}}$
So we can see that the velocity at the end is proportional to the $M/m$ ratio which is very high so the velocity at the end becomes very high.

Note:Potential energy of a system can be negative but Kinetic and Total energy of a system is always positive. Here sound energy is converted from another form of energy and obviously loud noise is a large amount of energy conversion.