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
\frac{l*450}{450} =\frac{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 !