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Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String

Three resonant frequencies of a string are observed to be 90 Hz , 150 Hz , and 210 Hz . If the string has a length of 80 cm , determine the speed of a transverse wave on this string.

Options

  1. A96 m s ⁻¹
  2. B72 m s ⁻¹
  3. C48 m s ⁻¹
  4. D24 m s ⁻¹

Correct answer

C. 48 m s ⁻¹

Step-by-step solution

For a string fixed at both ends, the resonant frequencies are given by: f_n = n v 2L where n = 1, 2, 3, and v is the speed of the transverse wave. The given observed resonant frequencies are 90 Hz , 150 Hz , and 210 Hz . These frequencies must be integer multiples of the fundamental frequency f₁ . To find the fundamental frequency, we take the highest common factor (HCF) of the given frequencies: f₁ = HCF (90, 150, 210) = 30 Hz The observed frequencies correspond to the 3rd, 5th, and 7th harmonics ( 3f₁, 5f₁, 7f₁ )

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