A violin string vibrates with fundamental frequency of 510 Hz. What is the frequency of first overtone? ( Ans: n1 = 1020 Hz )

Answer

To find the frequency of the first overtone of a violin string that vibrates with a fundamental frequency of 510 Hz, we can follow these steps:

### Step 1: Understand the Relationship Between Frequencies
The fundamental frequency (first harmonic) of a vibrating string is denoted as \( f_0 \). The first overtone (second harmonic) is denoted as \( f_1 \). The relationship between these frequencies is given by:
\[ f_1 = 2 f_0 \]

### Step 2: Substitute the Given Value
We know from the problem that the fundamental frequency \( f_0 \) is 510 Hz. We can substitute this value into the equation for the first overtone:
\[ f_1 = 2 \times 510 \text{ Hz} \]

### Step 3: Calculate the First Overtone
Now we perform the multiplication:
\[ f_1 = 1020 \text{ Hz} \]

### Step 4: Conclusion
Thus, the frequency of the first overtone is:
\[ \boxed{1020 \text{ Hz}} \]

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