Question

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

• A. $195Hz$
• B. $205Hz$
• C. $190Hz$
• D. $210Hz$

Answer 1

Answer: (B)

$205Hz$

Let the fundamental frequency of organ pipe be $f$ Hz

$f$ can be $195Hz$ or $205Hz$

Its second harmonic will be $390Hz$ or $410Hz$ correspondingly

out of which $410Hz$ can produce $10$ beats per second with a source of $420Hz$ frequency.

Hence, $f=205Hz$ .

option (b)