Q. A vibrating string of certain length I under a tension T resonates with a mode corresponding to the second overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generate 4 beats/s when excited along with a tuning fork of frequency n. now when the tension of the string also generate 4 beats/s when excited along with a tuning fork of frequency n. now when the tension of the string is slightly increased the number of beats reduces 2 per second. Assuming the velocity of sound in air to be $340ms^{- 1}$, the frequency n of the tuning fork in Hz is
A) 344
B) 336
C) 117.3
D) 109.3
Explanation
(a) With reflection in tension, frequency of vibrating string will increase. Since number of beats are decreasing. Therefore, frequency of vibrating string or third harmonic frequency of closed pipe should be less than the frequency of tuning fork by 4.
∴ frequency of tuning fork
= Third harmonic frequency of closed pipe+4
$= 3\left( \frac{v}{4\iota} \right) + 4 = 3\left( \frac{340}{4 \times 0.75} \right) + 4 = 344\ Hz$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.