In an organ pipe closed at one end, the sum of the frequencies of first three overtones is 3930 Hz . The frequency of the fundamental mode of organ pipe is

Step-by-step solution

For an organ pipe closed at one end, the harmonic frequencies are odd multiples of the fundamental frequency f₁ . The first three overtones correspond to the third, fifth, and seventh harmonics, with frequencies 3f₁ , 5f₁ , and 7f₁ , respectively. The sum of these overtone frequencies is given as 3930 Hz: 3f₁ + 5f₁ + 7f₁ = 3930 which simplifies to 15f₁ = 3930 Solving for f₁ : f₁ = 3930 15 = 262 Hz The fundamental frequency is 262 Hz , corresponding to option B.