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Answer: 525 cycles per second.
Step-by-step explanation:
The equation for inverse variation between x and y is given by :-
(1)
Given : The length of a violin string varies inversely with the frequency of its vibrations.
A violin string 14 inches long vibrates at a frequency of 450 cycles per second.
Let x = length of a violin
y= frequency of its vibrations
To find: The frequency of a 12 inch violin string.
Put in equation (1) , we get
Divide both sides by 12 , we get
Hence, the frequency of a 12 inch violin string = 525 cycles per second.
Set components equal:
From this we find:
Substitute and solve system:
The point where they intersect is:
From this we find:
Substitute and solve system:
The point where they intersect is: