Question

Define quality factor.

Answer 1

Hint: The students must remember that quality factor is a dimensionless quantity. So, it may be expressed as a ratio of two quantities having the same dimensions, or an approach may be taken by considering the fact that quality factor is something related to oscillations.

Complete step by step solution:
Definition:
In Physics, quality factor which is also named as Q-factor is a dimensionless parameter which describes the resonance behaviour of an under-damped harmonic oscillator. You might wonder what an under-damped oscillator is. So, in an oscillator, friction or damping slows down the motion of the system. In that case, the oscillations are categorized as damped oscillations. In a harmonic oscillator, we know that the force which acts is the restoring force, but if in addition to the restoring force, if we have frictional force (friction) acting on the harmonic oscillator, the oscillator is said to be damped, as the oscillations slow down. This is the case of a damped harmonic oscillator.
Now the quality factor of an oscillator which tells us how much damping is present in that oscillator. It is defined as follows:
$Q={\displaystyle \frac{{\omega }_r}{\mathrm{\Delta }\omega }}$
where Q is the quality factor of a given oscillator , ${\omega }_r$ signifies the resonant frequency of the oscillator while $\mathrm{\Delta }\omega$ is known as the full-width at half-maximum.

Additional information:
A damping coefficient is a parameter which indicates whether a material will bounce back or return energy to a system.

Note: The students must not be confused about un-damped and under-damped oscillations. The un-damped oscillations means the absence of a damping force while the system is executing oscillations, whereas under-damped oscillations are those which have been described above.