Question

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 1

Answer: 525 cycles per second.

Step-by-step explanation:

The equation for inverse variation between x and y is given by :-

$x_1y_1=x_2y_2$       (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 $x_1=14,\ x_2=12\\y_1=450,\ y_2=y$ in equation (1) , we get

$(14)(450)=(12)(y)$  

Divide both sides by 12 , we get

$y=\dfrac{(14)(450)}{12}=525$

Hence, the frequency of a 12 inch violin string = 525 cycles per second.