A horizontal string fixed at both ends vibrates in its fifth harmonic as y(x, t) = (0.01 m) sin[(62.8 m⁻¹)x] cos[(628 s⁻¹)t]. Take π = 3.14. Select the correct statements.
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Question

A horizontal string fixed at both ends vibrates in its fifth harmonic as y(x,t) = (0.01 m) sin[(62.8 m⁻¹)x] cos[(628 s⁻¹)t]. Take π = 3.14. Select the correct statements.

G1 Physics · Accepted Answer

Step 1: k=62.8 m⁻¹ and the string is in the 5th harmonic, so k=nπ/L gives L=5π/62.8=0.25 m. Step 2: At x=L/2, sin(kx)=sin(5π/2)=1, so maximum displacement is 0.01 m. Step 3: ω=628 s⁻¹ gives f=100 Hz for this harmonic, so fundamental is 20 Hz, not 100 Hz. Final: B and C.