Answer :
The frequency of a 12-inch violin string is 525 cycles per second.
The length (l) of a violin string is inversely proportional to the frequency (f) of its vibrations.
In other words, as the length of the string increases, the frequency decreases, and vice versa.
We are given that a violin string that is 14 inches long vibrates at a frequency of 450 cycles per second.
The frequency of a 12-inch violin string, we can set up an equation using the inverse variation formula:
l1 * f1 = l2 * f2
where l1 is the length of the first string (14 inches),
f1 is the frequency of the first string (450 cycles per second),
l2 is the length of the second string (12 inches),
and f2 is the frequency of the second string (which we need to find).
Plugging in the given values, we have:
14 * 450 = 12 * f2
Now we can solve for f2:
6300 = 12 * f2
Dividing both sides of the equation by 12:
f2 = 6300 / 12
Simplifying, we find:
f2 = 525
Hence, the frequency of a 12-inch violin string is 525 cycles per second.
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