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

As depicted in the figure, a string is stretched by a block going over a pulley. The string vibrates in its tenth harmonic in unison with a specific tuning fork. When a beaker containing water is positioned under the block such that the block becomes completely submerged, the string vibrates in its eleventh harmonic. Determine the density of the material of the block.

Options

  1. A4.8 10^3 kg/m ^3
  2. B5.8 10^3 kg/m ^3
  3. C5.2 10^3 kg/m ^3
  4. D1.1 10^4 kg/m ^3

Correct answer

B. 5.8 10^3 kg/m ^3

Step-by-step solution

The frequency of the n -th harmonic of a stretched string is given by: f = n 2L T where T is the tension in the string, L is its length, and is its linear mass density. Initially, the block is in the air, and the tension T₁ is equal to the weight of the block: T₁ = V g where V is the volume of the block and is its density. The string vibrates in its 10th harmonic, so the frequency is: f = 10 2L V g When the block is completely submerged in water, the tension T₂ is reduced due to the buoyant force: T₂ = V g - V _w g

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