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

A tuning fork with a frequency of 440 Hz is connected to a long string having a linear mass density of 0.01 kg m ⁻¹ and maintained under a tension of 49 N . The tuning fork generates transverse waves with an amplitude of 0.50 mm along the string. Determine the wave speed and the wavelength of these waves.

Options

  1. A70 m s ⁻¹ , 32 cm
  2. B140 m s ⁻¹ , 32 cm
  3. C35 m s ⁻¹ , 16 cm
  4. D70 m s ⁻¹ , 16 cm

Correct answer

D. 70 m s ⁻¹ , 16 cm

Step-by-step solution

Given parameters are: Frequency, f = 440 Hz Linear mass density, = 0.01 kg m ⁻¹ Tension, T = 49 N The wave speed v on a stretched string is given by: v = T Substituting the given values: v = 49 0.01 = 4900 = 70 m s ⁻¹ The wavelength is related to the wave speed and frequency by: = v f Substituting the values: = 70 440 m = 7 44 m Converting to centimeters: = 700 44 cm 15.9 cm 16 cm The wave speed is 70 m s ⁻¹ and the wavelength is 16 cm .

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