Q. Two uniform wires are vibrating simultaneously in their fundamental notes. The tension , lengths diameters and the densities of the two wires are in the ratio 8:1, 36:35, 4:1,and 1:2 respectively. If the note of the higher pitch has a frequency 360 Hz, the number of beats produced per second is
A) 5
B) 15
C) 10
D) 20
Explanation
(c) Here , $\frac{T_{1}}{T_{2}} = \frac{8}{1},\frac{l_{1}}{l_{2}} = \frac{36}{35},\frac{D_{1}}{D_{2}} = \frac{4}{1}$
and $\frac{\rho_{1}}{\rho_{2}} = \frac{1}{2}$
$n_{1} = 360\ Hz,\ n_{2} = ?$
Now, $\frac{n_{2}}{n_{1}} = \frac{l_{1}D_{1}}{l_{2}D_{2}}\sqrt{\frac{T_{2}\rho_{1}}{\rho_{2}T_{1}}}$
$\frac{n_{2}}{n_{1}} = \frac{36}{35} \times \frac{4}{1}\sqrt{\frac{1}{8} \times \frac{1}{2}} = \frac{36}{35}$
Clearly $n_{2} > n_{1}$. When $n_{2} = 360\ Hz;n_{1} = 350\ Hz$
Number of beats $s^{- 1} = n_{2} - n_{1} = 360 - 350 = 10$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.