SOMEONE PL HEL. When under equal tension, the frequency of a vibrating string in a piano varies inversely with the string length. If a string that is 410 millimeters in length vibrates at a frequency of 515 cycles a second, at about what frequency will a 705-millimeter string vibrate?

299.5 cycles per second.

Step-by-step explanation:

An inverse variation can be written as:

y = k/x

Where, in this case:

y = frequency

x = length of the string

k = constant.

We know that 410 mm correspond to 515 cps.

then:

515cps = k/410mm

k = 515cps*410mm = 211,150 cps*mm

now, if we use x = 705mm we can find the frequency as:

y = ( 211,150 cps*mm)/705mm = 299.5 cycles per second.

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32