Strings set to vibration using same tuning fork

Question

Identical strings start vibrating in !!1^(st)!!(A) and !!3^(rd)!!(B) harmonic mode due to the same tuning fork. The tension in strings is related by:

  • !!T_A=3T_B!!
  • !!3T_A=T_B!!
  • !!T_A=9T_B!!
  • !!9T_A=T_B!!

Solution

Since the 2 strings are set to vibration using the same tuning fork they are vibrating at the same frequency.

If the length of the string is !!l!!, mass !!m!! and tension in the string is !!T!!.

The frequency of the vibrations can be given by:

!!n=1/(2l)sqrt(T_A/m)!!

!!n=3xx1/(2l)sqrt(T_B/m)!!

So !!T_A=9T_B!!

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