Question

a 2.00m piano wire with a mass per unit length of 12.0 g/m is under tension of 8.00 kN and fixed at both ends.

The second harmonic is defined as the vibration mode with two antinode. What is the time period of oscillation when the string Is vibrating in the second harmonic mode?

Answer 1

Speed of the wave in the string, v = T/m

Where, T = 8 kN = 8*103 N,

m = 12 g/m = 12*10-3 kg/m

Thus, speed, v = 8*103/12*10-3 = 816.49 m/s

When vibrating in second harmonic, we have,

Wavelength, = length of the wire = 2 m

So, time period, T = /v = (2/816.49) s

= 2.45*10-3  s

= 2.45 ms