Direct visualization of mechanical beats by means of an oscillating smartphone
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.