Q: Two closed-end pipes, when sounded together produce 5 beats/s. If their lengths are in the ratio 100:101, then fundamental notes (in Hz) produced by them are

(a) 245, 250

(b) 250, 255

(c) 495, 500

(d) 500, 505

Ans: (d)

Sol: Frequency $ \displaystyle f \propto \frac{1}{L}$

$\displaystyle \frac{f_1}{f_2} = \frac{L_2}{L_1} $

$ \displaystyle \frac{f_1}{f_2} = \frac{101}{100} $ ..(i)

As , $ \displaystyle f_1 – f_2 = 5 $ …(ii)

Solve (i) & (ii)