A string of length 1.8 m and mass 0.036 kg has a fundamental frequency of 50 Hz. What is the tension in the string?
**Transverse wave velocity** depends on medium not frequency alone. For string under tension, v ∝ √(T/μ), calculation requires μ from mass and length, then square root evaluation, giving v in m/s, then f = v/λ for given wavelength. μ = (0.036/1.8) = 0.02 kg/m . v₁ = (v/2L) ⇒ 50 = (v/2 × 1.8) ⇒ v = 50 × 3.6 = 180 m/s . v = √((T/μ)) ⇒ 180 = √((T/0.02)) ⇒ 180² = (T/0.02) . T = 32400 × 0.02 = 648 N . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 648 N, illustrating
Ref: NCERT > Physics Book > Waves > Wave Speed, Energy and Power
