Two tuning forks produce sounds with frequencies of \( 256 \ \text{Hz} \) and \( 260 \ \text{Hz} \). What is the beat frequency?
\[ f_{\text{beat}} = |260 - 256| = 4 \ \text{Hz} \]
Answer: 4 beats per second are heard.
Beats are a phenomenon that occurs when two sound waves of slightly different frequencies interfere with each other. The result is a fluctuating volume (alternating loud and soft sounds) known as beats.
The beat frequency is the number of volume fluctuations heard per second and is given by:
\[ f_{\text{beat}} = |f_1 - f_2| \]
Beats are commonly used to tune musical instruments by matching the frequencies until the beats disappear (indicating that both frequencies are equal).
Two tuning forks produce sounds with frequencies of \( 256 \ \text{Hz} \) and \( 260 \ \text{Hz} \). What is the beat frequency?
\[ f_{\text{beat}} = |260 - 256| = 4 \ \text{Hz} \]
Answer: 4 beats per second are heard.
Harmonics are the natural frequencies at which an object (like a string or pipe) tends to vibrate. The fundamental frequency is the lowest harmonic and determines the pitch of the sound. Higher harmonics are whole-number multiples of the fundamental frequency.
For an open pipe (open at both ends):
For a closed pipe (closed at one end):
The frequency of each harmonic is given by:
\[ f_n = n \cdot f_1 \]
A string of length \( L = 1.2 \ \text{m} \) is fixed at both ends. The speed of the wave on the string is \( 240 \ \text{m/s} \). What is the frequency of the fundamental and the second harmonic?
Step 1: Find Fundamental Frequency (1st harmonic)
\[ f_1 = \frac{v}{2L} = \frac{240}{2 \times 1.2} = 100 \ \text{Hz} \]
Step 2: 2nd Harmonic
\[ f_2 = 2 \cdot f_1 = 2 \cdot 100 = 200 \ \text{Hz} \]
Answer: \( f_1 = 100 \ \text{Hz} \), \( f_2 = 200 \ \text{Hz} \)
Written by Thenura Dilruk