A metallic rod of length 1 m has one end free and the other rigidly clamped. Longitudinal stationary waves are present with six antinodes. Antinode amplitude is 4 × 10⁻⁶ m, Young's modulus is 6.4 × 10¹⁰ N m⁻² and density is 4 × 10³ kg m⁻³. The free end is x = 0 and at t = 0 it is at positive extreme.

Options

• Option A

  s = 4×10⁻⁶ cos(11πx/2) cos(22π×10³t)

• Option B

  s = 4×10⁻⁶ cos(11πx/2) sin(22π×10³t)

• Option C

  s = 4×10⁻⁶ cos(5πx) cos(20π×10³t)

• Option D

  s = 4×10⁻⁶ cos(5πx) sin(20π×10³t)

Options

• Option A

  σ = 140.8π×10⁴ cos(11πx/2 + π) cos(22π×10³t)

• Option B

  σ = 140.8π×10⁴ sin(11πx/2 + π) cos(22π×10³t)

• Option C

  σ = 128π×10⁴ cos(5πx + π) cos(20π×10³t)

• Option D

  σ = 128π×10⁴ sin(5πx + π) cos(20π×10³t)

Options

• Option A

  11√3π×10⁻⁶

• Option B

  11√2π×10⁻⁶

• Option C

  10√3π×10⁻⁶

• Option D

  10√2π×10⁻⁶