A steel wire with mass per unit length 7.0 × 10⁻³ kg m⁻¹ is under tension of 70 N. The speed of transverse waves in the wire will be:

Solution

Physics sir · 3 steps

Speed on a string needs only two things: tension on top, mass per unit length below, then a square root.

1. The formula. For a transverse wave on a stretched string, the tension pulls the string back and the mass per unit length resists the motion. Together they fix the wave speed.

   v = √(T/μ)

2. Put in numbers. T/μ = 70/(7.0 × 10⁻³) = 1.0 × 10⁴ m² s⁻², so v = √10⁴ = 100 m s⁻¹.
3. So. The transverse waves travel at 100 m s⁻¹, which is option (c).

The idea to keep. For any string wave, use v = √(T/μ). Check the power of ten in μ before dividing, and remember the square root comes last.

Answer from the NTA final answer key. Solution by PrepWiser.