Fourier analysis of a vibrating string through a low-cost experimental setup and a smartphone

Abstract

In this work we present a simple and low-cost setup to illustrate the dependence of the behaviour of a standing wave in a guitar string with the initial conditions. To do so, we impose two kinds of initial conditions; in the first instance, the initial shape of the string is varied. Secondly, different nodes are imposed on the string. This dependence was studied using the Fourier analysis of the sound produced by the vibration of the string with a smartphone. The simplicity of the proposed activity makes it suitable to be implemented in any classroom to illustrate the concept of normal modes and as an example of Fourier series in a real system that is also familiar for the students.

Effect of Real-time Physics Organizer Based Smartphone and Indigenous Technology to Students’ Scientific Literacy Viewed from Gender Differences

“…Consistent with the research of Pereyra et al (2018), in the experiment group students can recognize that an idea of science can change when new evidence is found and can be derived from observations of phenomena in nature, for example, students initially assume that many objects are similar to the string will only produce a single frequency spectrum and Melde's Law is difficult to explore, however after using RPO it can be explored easily. Students become enthusiastic to find problems solutions.…”

“…Smartphones have reached the traditional community (Roslinda, 2016), however, their use for physics experimentation is still very unfamiliar. Experimentation using modern musical instruments and smartphones as in the research of Konz & Ruiz (2018), Pereyra et al (2018), andYavuz (2015) can be difficult for students from other countries or regions to realize. Students in West Borneo for example, are still more familiar with traditional musical instruments such as Senggayung and Sape' (Suma, 2007;Yusufarief1, 2017).…”

Teaching Fourier series with tone experiments based on smartphone applications

“…Smartphones can also be developed as low-cost measurement or sensing systems suitable for conducting experiments owing to their high-performance microprocessors and various sensors inside them [13], such as highresolution cameras, microphones, accelerometers, gyroscopes, magnetometers, GPS, flashlights, and loudspeakers [20]. Many teachers use smartphone applications (APP) to conduct experiments to assist teaching [16], such as vibration experiments [17], physics experiments [17,19,30], magnetic field measurements [23], signal and system laboratories [18], and Fourier analysis [24,26]. Some teachers even developed interactive APPs suitable for their own courses to assist teaching and improve learning outcomes [9,10].…”

“…Some teachers even developed interactive APPs suitable for their own courses to assist teaching and improve learning outcomes [9,10]. In [24], a smartphone Android APP (Spectroid) to perform a Fourier analysis of the sound produced by a guitar. It allows students to observe the properties of string sounds both scientifically and experimentally.…”

Coupled oscillations of the Wilberforce pendulum unveiled by smartphones

“…While the original purpose of the device was the measurement of spring constants, the Wilberforce pendulum is currently used in physics teaching at Universities to illustrate a wide variety of concepts regarding oscillatory phenomena, including coupling, normal modes or beats, among others [3,[5][6][7][8][9]. In recent years the study of these fundamental concepts has been approached with the use of smartphones [10][11][12].…”