Physics Demonstrations

Sound Wave

Frequency 1 (Hz)
Amplitude 1
Frequency 2 (Hz)
Amplitude 2

In this demonstration, we explore the superposition of two traveling sound waves. Each wave has a frequency ( $f_{1}$ , $f_{2}$ ) and amplitude ( $A_{1}$ , $A_{2}$ ). The displacement of each traveling wave as a function of position and time is: $y_{1} (x, t) = A_{1} \cdot \sin (2 π f_{1} x - 2 π f_{1} t)$ $y_{2} (x, t) = A_{2} \cdot \sin (2 π f_{2} x - 2 π f_{2} t)$ By the Principle of Superposition, the resultant wave is the sum: $y = y_{1} + y_{2}$ When the two frequencies are close but not equal, the superposition produces beats — a periodic variation in amplitude at the beat frequency: $f_{beat} = \| f_{1} - f_{2} \|$ The top two panels show each individual wave; the bottom panel shows their superposition. The title displays the computed beat frequency. Some questions to consider while viewing the demonstration: Set $f_{1} = f_{2}$ . What does the superposition look like? What happens to the beat frequency? Set $f_{1} = 5$ and $f_{2} = 6$ . How many amplitude peaks appear per second in the superposition? How does changing the amplitudes affect the superposition when the two waves are out of phase? Identify a real-world situation where beats are heard between two sound sources.