A steel wire in a piano has a length of 0.540 m and a mass of 4.800 ✕ 10−3 kg. To what tension must this wire be stretched so that the fundamental vibration corresponds to middle C (fC = 261.6 Hz on the chromatic musical scale)?

T = 708.81 N

Explanation:

Given that,

Length of a steel wire in a piano, l =0.54 m

Mass,

We need to find the tension must this wire be stretched so that the fundamental vibration corresponds to middle C, fc = 261.6 Hz

The equation for fundamental frequency is given by :

So, the required tension in the wire is 708.81 N.

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min