The fourth harmonic of a fundamental frequency is 512 Hz. What is the fundamental frequency?
128 Hz
Understanding Harmonic Frequencies
In physics, especially when dealing with sound waves or vibrating strings, a harmonic is an integer multiple of the fundamental frequency. The fundamental frequency is the lowest natural frequency of a vibrating object or system. It is also known as the first harmonic.
When a string or an air column vibrates, it can vibrate at its fundamental frequency and also at higher frequencies that are whole number multiples of the fundamental frequency. These higher frequencies are called overtones, and if they are integer multiples of the fundamental frequency, they are also called harmonics.
- The first harmonic is the fundamental frequency itself ($\text{n}=1$).
- The second harmonic is twice the fundamental frequency ($\text{n}=2$).
- The third harmonic is three times the fundamental frequency ($\text{n}=3$).
- And so on.
Harmonic Frequency Formula
The relationship between any harmonic and the fundamental frequency can be expressed using a simple formula:
\[ f_n = n \times f_1 \]
Where:
- \(f_n\) is the frequency of the \(n\)-th harmonic.
- \(n\) is the harmonic number (an integer: 1, 2, 3, ...).
- \(f_1\) is the fundamental frequency.
Calculating Fundamental Frequency
The question provides us with the frequency of the fourth harmonic and asks us to find the fundamental frequency. Let's list the given information:
- The fourth harmonic frequency (\(f_4\)) = 512 Hz.
- The harmonic number (\(n\)) = 4.
We need to find the fundamental frequency (\(f_1\)).
Using the harmonic frequency formula:
\[ f_n = n \times f_1 \]
Substitute the given values into the formula:
\[ 512 \text{ Hz} = 4 \times f_1 \]
To find \(f_1\), we need to divide the fourth harmonic frequency by the harmonic number (4):
\[ f_1 = \frac{512 \text{ Hz}}{4} \]
Performing the division:
\[ f_1 = 128 \text{ Hz} \]
Therefore, the fundamental frequency is 128 Hz.
Important Questions from Standard Signals
The properties of Dirac Delta are
A. δ (t - to)=∞ if t = to
B. δ (t - to)=0 if t = to
C. δ (t - to)=0 if t ≠ to
D. δ (t - to)=∞ if t ≠ to
E. δ (t - to)=1 for all t = to
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