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

A wire fixed at both its ends is found to vibrate at resonant frequencies of 240 Hz and 320 Hz . If transverse waves travel on this string at a speed of 40 m s ⁻¹ , what is the length of the string?

Options

  1. A12.5 cm
  2. B50 cm
  3. C6.25 cm
  4. D25 cm

Correct answer

D. 25 cm

Step-by-step solution

For a string fixed at both ends, the resonant frequencies are given by f_n = nv 2L , where n is an integer representing the harmonic number, v is the wave speed, and L is the length of the string. Assuming the given frequencies are consecutive resonant frequencies, their difference gives the fundamental frequency f₁ : f₁ = f_ n+1 - f_n f₁ = 320 Hz - 240 Hz = 80 Hz The fundamental frequency is also given by the formula: f₁ = v 2L Substituting the given values ( f₁ = 80 Hz and v = 40 m s ⁻¹ ): 80 = 40 2L 160L = 40 L

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