A tube 1m long is closed at one end.A wire of length 0.3m and mass 1×10^-2kg is stretched between two fixed ends and is placed near the open end. When the wire is plucked at its mid pt the air column resonates in its 1st overtone. Find the tension in the wire if it vibrates in its fundamental mode.
Since air Column is vibrating in it’s 1st overtone so it’s frequency must be
f= 3v/4l
v is velocity of sound in air and l is length of air column.
Taking sound velocity in air as 330 m/s and length given is 1m. Putting these value frequency will come= 990/4=247.5Hz
Now for string, It’s fundamental frequency would be
f=V/2l =√(T/µ)/2l
Where T is tension µ is mass density and l is length of wire
Putting all the value and equating it with 247.5Hz we get
T=735 N