Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String
Three resonant frequencies of a string are measured as 90 Hz , 150 Hz , and 210 Hz . Determine which overtones these given frequencies represent.
Options
- A1st, 3rd, and 5th
- B2nd, 3rd, and 4th
- C3rd, 5th, and 7th
- D2nd, 4th, and 6th
Correct answer
D. 2nd, 4th, and 6th
Step-by-step solution
The given resonant frequencies of the string are 90 Hz , 150 Hz , and 210 Hz . The fundamental frequency f₀ is the highest common factor (HCF) of these frequencies. f₀ = HCF (90, 150, 210) = 30 Hz The harmonic numbers corresponding to the given frequencies are: n₁ = 90 30 = 3 (3rd harmonic) n₂ = 150 30 = 5 (5th harmonic) n₃ = 210 30 = 7 (7th harmonic) For a string fixed at both ends, the n^ th harmonic corresponds to the (n-1)^ th overtone. Therefore, the 3rd, 5th, and 7th harmonics correspond to the 2nd, 4th, and