Question

What does amplitude measure?

Answer 1

Hint: The amplitude is a parameter of a wave which gives the idea of the structure of the wave. First we need to define amplitude of a wave and its physical meaning on the graph. Further according to the graph of the variation of the dependent variable with respect to the independent variable we can determine what does the amplitude measure.
Formula used:
$y=A\sin (\omega t-kx)$

Complete step-by-step solution:
The amplitude of a wave gives an idea that what is the maximum value of any quantity with respect to the independent variable or the quantity of consideration varying in a sinusoidal fashion. If the amplitude of the wave is ‘A’, with angular frequency $\omega $ and propagation constant k, then the variation of the wave with ‘x’ and ‘y’ with time ‘t’ is given by,
$y=A\sin (\omega t-kx)$
Let us say we want to interpret a sound wave. Let us say the equation gives the variation of intensity with time . If the sound wave is propagating in space so that it does not lose energy then we can say that greater the amplitude of the sound wave better will be the loudness of the sound. Similarly if we wish to interpret the position of the bob in a pendulum with respect to mean position, then the amplitude determines what is the maximum distance of the bob from the mean position.
From the above interpretation, we can conclude that the amplitude basically measures the maximum value of a quantity with respect to independent quantity, having its own significance.

Note: The amplitude of the wave actually originated from the sound wave itself. Higher the amplitude basically means greater is the energy required to generate the sound wave and hence louder the sound would be. If you strike a thin metal surface, the particle vibrates with greater amplitude thereby the sound being more louder.