Understanding Beats in Sound: The Case of Tuning Forks with Frequencies 100 Hz, 101 Hz, and 102 Hz
Introduction
When multiple sound frequencies are played together, a phenomenon called ldquo;beatsrdquo; occurs. This article explores the concept of beats using three tuning forks with specific frequencies100 Hz, 101 Hz, and 102 Hz. We will delve into the mathematical calculations and derive the number of beats heard per second when these tuning forks are sounded together.
Concept of Beats in Sound
The phenomenon of beats is the result of the interference between two or more sound waves of slightly different frequencies. The number of beats heard per second is equal to the absolute value of the difference in frequencies of the sound waves.
Calculation of Beats
Letrsquo;s consider three tuning forks with the following frequencies:
f_1 100 , text{Hz} f_2 101 , text{Hz} f_3 102 , text{Hz}We can determine the number of beats by calculating the differences between each pair of frequencies:
Beat Frequencies between Pairs of Frequencies
f_1 - f_2 100 - 101 1 , text{Hz} f_2 - f_3 101 - 102 -1 , text{Hz} (absolute value: 1 Hz) f_1 - f_3 100 - 102 -2 , text{Hz} (absolute value: 2 Hz)Summing the individual beat frequencies:
From 100 Hz and 101 Hz: 1 beat per second From 101 Hz and 102 Hz: 1 beat per second From 100 Hz and 102 Hz: 2 beats per secondThe relevant beats heard are the highest frequency beat. Therefore, the total number of beats heard in one second will be:
2 beats per second
Interference and Regularity of Beats
If we consider the superposition of waves, we would find that the interference between 100 Hz and 101 Hz creates one beat per second. Similarly, the interference between 101 Hz and 102 Hz also creates one beat per second. The interference between 100 Hz and 102 Hz creates two beats per second.
However, if all the interference patterns were synchronized, you would hear two beats per second but one would be much louder because it would be reinforced two more times.
But synchronizing all the patterns is highly unlikely. In reality, you would hear:
2 beats from 100 Hz and 102 Hz 1 beat from 100 Hz and 101 Hz 1 beat from 101 Hz and 102 HzThis results in a total of four beats per second. The beats would not be regularly spaced, with the exception of the two-beat interference, which would be evenly spaced at 2 beats per second.
Conclusion
The phenomenon of beats in sound leads to a fascinating interplay of frequency differences and interference patterns. By understanding the math behind the beats, we can predict and explain the auditory experiences when tuning forks with specific frequencies are sounded together.