  The resonance phenomenon is widely known from Physics courses. Qualitatively
speaking, it takes place in a driven oscillating system whenever the driven
frequency approaches the natural frequency. It is when the amplitude of the
oscillations become maximal. Very closely related to this phenomenon, there is
another which is very surprising too. It takes place when the driven and
natural frequencies of the system are slightly different and interfere
constructively and destructively, forming the so called beats. The frequency of
the beats is just the difference of the interfering waves frequencies. Beats
are very noticeable in acoustic systems. We all have probably perceived them in
the form of periodic ups and downs in the sound intensity volume. There are
several works in this journal on visualizing the beats in acoustic systems. For
instance, the microphone and the speaker of two mobile devices were used in
previous work to analyze the acoustic beat produced by two signals of close
frequencies. The formation of beats can also be visualized in mechanical
systems, such as a mass-spring system5 or a double driven string. Hereafter,
the mechanical beats in a smartphone-spring system are directly visualized in a
simple way. The frequency of the beats is measured by means of the acceleration
sensor of a smartphone which hangs from a spring attached to a motor driver.

Physics Education