Third harmonic standing wave on fixed string

Steps:

• Length L = 1.35 m fits 3 half-wavelengths for third harmonic (n=3, as implied by diagram).
• Wavelength λ = 2L/n = 2 × 1.35 / 3 = 0.9 m.
• Frequency f = speed / wavelength = 450 m/s / 0.9 m = 500 Hz.
• Matches option C.

Why C is correct:

• Standing wave frequency for nth harmonic is f_n = n v / (2L); for n=3, f=3×450/(2×1.35)=500 Hz.

Why the others are wrong:

• A: Second harmonic (n=2), f=2×450/2.7=333 Hz.
• B: Does not match any integer harmonic frequency.
• D: Sixth harmonic (n=6), f=6×450/2.7=1000 Hz.

Final answer: C