A string has three resonant frequencies at 90 Hz , 150 Hz , and 210 Hz . Determine the highest possible fundamental frequency of vibration for this string.

Step-by-step solution

The resonant frequencies of a vibrating string are integer multiples of its fundamental frequency f₀ . Let the given resonant frequencies be f₁ = 90 Hz , f₂ = 150 Hz , and f₃ = 210 Hz . We have f₁ = n₁ f₀ , f₂ = n₂ f₀ , and f₃ = n₃ f₀ , where n₁, n₂, n₃ are integers. The highest possible fundamental frequency is the highest common factor (HCF) of the given resonant frequencies. f₀ = HCF (90, 150, 210) 90 = 30 3 150 = 30 5 210 = 30 7 The highest common factor is 30 . Thus, the highest possible fundamental frequency