Question

The number of vibrations in a piano string are inversely proportional to its length. A wire 1.25m long vibrates at 510 vibrations/second. To produce 450 vibrations per second, how long should a wire be made

Answer 1

Let's assume number of vibrations in a piano strings be v and length is l.

Given that, A wire 1.25m long vibrates at 510 vibrations/second.

So, l = 1.25 and v = 510.

The number of vibrations in a piano string are inversely proportional to its length. So, we can set up an equation as following:

l*v = k

1.25 * 510 = k

637.5 = k

Therefore, the equation will be l*v =637.5.

Now we need to find the length of wire: l for the vibration: v = 450.

So, plug in v=450 in the above equation to get the value of l. Therefore,

l * 450 = 637.5

`(l*450)/(450) =(637.5)/(450)`

l = 1.4167

l = 1.42 ( Rounded to hundredth).

So, length of wire is 1.42 m long.

Hope it's help you !