If a sonometer has a fundamental frequency of 450HZ, what is the frequency of the fifth overtone?

Analyze the question: A sonometer is a stretched string fixed at both ends. We're given the fundamental frequency (f₀ = 450 Hz) and asked for the fifth overtone.

Concept: For a string fixed at both ends, all harmonics are present:

• 1st harmonic = fundamental = f₀
• 1st overtone = 2nd harmonic = 2f₀
• 2nd overtone = 3rd harmonic = 3f₀
• nth overtone = (n + 1) f₀

The key point is that the overtone number is always one less than the harmonic number.

Solution:

• Fifth overtone = 6th harmonic
• f = 6 × f₀ = 6 × 450 = 2700 Hz

Answer: The fifth overtone is 2700 Hz, which matches option A.

Tip: Remember "overtone = harmonic − 1". The first overtone is the second harmonic, so the fifth overtone is the sixth harmonic. Many students wrongly multiply by 5 (giving 2250 Hz), which is not among the options. Options B, C and D are distractors that don't follow from any multiple of 450 Hz.