Sound pendulum
Exploring Sound Waves: Interactive Pendulum Experiment to Understand the Doppler Effect
Author:
Title 4
Learning objectives :
This activity allows students to understand the Doppler effect by analyzing the frequency variations of a sound emitted by a moving pendulum. It develops the ability to interpret a complex acoustic phenomenon.
Concepts covered
Doppler effect; Frequency and period; Pendulum movement; Variable speed; Spectral analysis
What students will do :
The student studies the frequency variations of a sound emitted by a smartphone suspended in a pendulum movement or uses the 'Doppler Pendulum Effect' recording from the FizziQ library. By carefully analyzing the characteristics of the sound, the student determines the frequency emitted, the oscillation period and the maximum speed of the pendulum, then reflects on the asymmetry observed in the frequency curve.
What is required :
Smartphone with the FizziQ application; Wire or string for hanging a smartphone (option 1); Recording 'Doppler Pendulum Effect' from the sound library (option 2); FizziQ experience notebook
Scientific background :
The Doppler effect, discovered by Christian Doppler in 1842, is the apparent variation in frequency of a wave perceived by an observer when the source and the observer are in relative motion. For a sound source approaching the observer, the perceived frequency is higher than the emitted frequency; when it moves away, the perceived frequency is lower. In the case of a sound pendulum, the source (smartphone) oscillates back and forth from a point of balance, creating a periodic movement of approach and distance. The apparent frequency f' is linked to the emitted frequency f by the relation: f' = f × (1 + v/c), where v is the component of the speed of the source in the direction of the observer (positive when approaching, negative when moving away) and c is the speed of sound (approximately 343 m/s at 20°C). For a simple pendulum, the speed varies continuously: zero at the ends of the oscillation and maximum at the equilibrium point. This variation in speed results in a modulation of the perceived frequency, creating a characteristic "rise-fall" pattern of the frequency. The asymmetry observed in the frequency curve is explained by two main factors: 1) The projection of the pendulum's speed towards the observer is not sinusoidal but depends on the position of the observer; 2) The relationship between speed and frequency is not linear but fractional, which accentuates the variations. Knowing the base frequency f and the maximum amplitude of the shift Δf, we can calculate the maximum speed of the pendulum: v_max = c × Δf/f. If the transmitted frequency is 1000 Hz and the maximum variation observed is ±3 Hz, the maximum speed of the pendulum is approximately 1 m/s. This experiment illustrates a phenomenon also observed in many contexts: passing ambulance sirens, astronomical Doppler effect, and even medical imaging by Doppler ultrasound.