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