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. Find the frequency of a 12 inch violin string.

Answer: 525 cycles per second.Step-by-step explanation:The equation for inverse variation between x and y is given by :-[tex]x_1y_1=x_2y_2[/tex]       (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 violiny=  frequency of its vibrationsTo find: The frequency of a 12 inch violin string.Put [tex]x_1=14,\ x_2=12\\y_1=450,\ y_2=y[/tex] in equation (1) , we get[tex](14)(450)=(12)(y)[/tex]   Divide both sides by 12 , we get[tex]y=\dfrac{(14)(450)}{12}=525[/tex] Hence, the frequency of a 12 inch violin string = 525 cycles per second.