Standing wave produced in a metal rod of length 1 m fixed at the left end is represented by the equation
$y = 1 0^{- 6} sin \frac{π x}{2} sin 200 π t$
where x and y are in metre and t is in seconds. The maximum tensile stress at the midpoint of the rod is : (Young's modulus of material of rod $= 1 0^{12} N / m^{2}$ )

Question

Standing wave produced in a metal rod of length 1 m fixed at the left end is represented by the equation

$y = 1 0^{- 6} sin \frac{π x}{2} sin 200 π t$

where x and y are in metre and t is in seconds. The maximum tensile stress at the midpoint of the rod is : (Young's modulus of material of rod $= 1 0^{12} N / m^{2}$ )

TestHub · Accepted Answer

Stress = Y x strain, with strain ∂ x ∂ y ​ = 1 0 − 6 ⋅ 2 π ​ cos 2 π x ​ sin 200 π t At the midpoint x = 0.5 m: cos 4 π ​ = 2 ​ 1 ​ σ ma x ​ = 1 0 12 × 1 0 − 6 × 2 π ​ × 2 ​ 1 ​ = 2 2 ​ π ​ × 1 0 6 N/ m 2 Answer: C

Physics - Sound Wave Question with Solution | TestHub

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JEE Main 2027 (Class 12)