A sonometer wire is kept taut by a metal block hanging from its end, and it vibrates at in its fundamental mode. The block is now completely immersed in water. If the density of the metal is times that of water, what is the new fundamental frequency?

Answer and explanation

Correct answer: C. 299.3 Hz

  1. Step 1: The fundamental frequency of a sonometer wire of fixed length and linear mass density is proportional to the square root of string tension: .
  2. Step 2: When the metal block of mass and density is completely immersed in water, it experiences an upward buoyant force equal to the weight of displaced water: .
  3. Step 3: The net apparent tension in the wire becomes .
  4. Step 4: Calculate the new fundamental frequency: .
Answer
299.3 Hz.
Why not the others: incorrectly assumes frequency depends linearly on tension () rather than on its square root.

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