The speed of a transverse wave, going on a uniform wire having a length 50 cm and mass 5.0 g, is 80 m/s. The area of cross-section of the wire is 1.0 mm² and its Young’s modulus is 16 × 10⁹ N/m². Find the extension (in mm) of the wire over its natural length.
Physics · Mixed Chapter
JEE Mains

Question

The speed of a transverse wave, going on a uniform wire having a length 50 cm and mass 5.0 g, is 80 m/s. The area of cross-section of the wire is 1.0 mm² and its Young’s modulus is 16 × 10⁹ N/m². Find the extension (in mm) of the wire over its natural length.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Linear density is μ=0.005/0.5=0.01 kg m⁻¹, so tension required for transverse-wave speed 80 m/s is F=μv²=64 N. Step 2: Extension is ΔL=FL/(AY). Put F=64 N, L=0.5 m, A=10⁻⁶ m² and Y=16×10⁹ N/m². Step 3: ΔL=(64×0.5)/(10⁻⁶×16×10⁹)=0.002 m. Step 4: ΔL=2 mm.