Fundamental Frequency of a Well – Rankers Physics
Topic: Waves
Subtopic: Standing Wave in String and Organ Pipe

Fundamental Frequency of a Well

A person hums in a well and finds strong resonance at frequencies \(180\text{ Hz}\), \(300\text{ Hz}\) and \(420\text{ Hz}\). The fundamental frequency of the well is (velocity of sound \(= 335\text{ m/s}\))
180 Hz
100 Hz
60 Hz
120 Hz

Solution:

A well acts as a closed organ pipe. The resonant frequencies are odd harmonics: \(f_n = (2n-1)f_1\). The difference between consecutive resonant frequencies is \(300 - 180 = 120\text{ Hz}\), which corresponds to \(2f_1\). Thus, \(f_1 = 60\text{ Hz}\).

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