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

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

Tardigrade Admin · Accepted Answer

Let the fundamental frequency of organ pipe be

f

Case

I : f = 200 \pm 5 = 205 Hz

or

195 Hz

Case II: frequency of

2^{n d}

harmonic of organ pipe

= 2 f

(as is clear from the second figure)

2 f = 420 \pm 10

or

f = 210 \pm 5

or

f = 205

or

215

Hence fundamental frequency of organ pipe

= 205 Hz

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

195 HZ

205 HZ

190 HZ

210 HZ

Let the fundamental frequency of organ pipe be f Case I:f=200±5=205Hz or 195Hz 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 =205Hz

Q. 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