Example 1 · level 1
A sitar string has linear mass density 0.005 kg/m and is under a tension of 450 N. Find the speed of transverse waves on it (in m/s).
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- v = √(450 ÷ 0.005) = √90000 = 300 m/s.
Answer: 300
CLASS 11–12 PHYSICS · WAVES
Waves: strings and air columns
Speed on a string v = √(T/μ). Fundamental of a string fixed at both ends or an open pipe: f = v/2L; closed pipe: f = v/4L.
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Worked examples
Example 2 · level 2
A flute (treated as a pipe open at both ends) is 0.75 m long. Speed of sound = 320 m/s. Find the frequency of its fundamental (in Hz, correct to 2 decimal places).
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- f₁ = 320 ÷ 1.5 = 213.33 Hz.
Answer: 213.33 Hz
Example 3 · level 3
A flute (treated as a pipe open at both ends) is 0.5 m long. Speed of sound = 320 m/s. Find the frequency of its third harmonic (in Hz, correct to 2 decimal places).
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- f₁ = 320 ÷ 1 = 320 Hz.
- f₃ = 3 × 320 = 960 Hz.
Answer: 960 Hz