Question

An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency 200 Hz. The second harmonic of the same pipes produces 10 beats per second with a source of frequency 420 Hz. The fundamental frequency of organ pipe is 

(a) 195 Hz 

(b) 205 Hz 

(c) 190 Hz 

(d) 210 Hz

Answer 1

Correct option: (b) 205 Hz

Explanation: 

Let the fundamental frequency of organ pipe be f 

Case I : f = 200 ± 5 = 205 Hz or 195 Hz

Case II : frequency of 2nd harmonic of organ pipe = 2f (as is clear from the second figure) 

2f = 420 ± 10 or f = 210 ± 5 or f = 205 or 215 

Hence fundamental frequency of organ pipe = 205 Hz