What expression gives the wavelength of the third harmonic for a 1.5 m pipe that is closed at one end?

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11ecba2d_1312_da6a_a3bf_d3ea7d476b1a_MD0008_00 Like other acoustic objects, physically perturbed pipes generate standing waves that form in accordance with the shape and dimensions of the perturbed object. The multiple standing waves elicited in pipes develop in a fixed series known as harmonics. For example, the unique acoustic qualities of a wind instrument (ie, a musical instrument built from an open or closed pipe) are derived from the unique harmonic series of that particular instrument. The wavelength of the first harmonic (λ₁) corresponds to the soundwave of the longest wavelength that may be produced within a pipe. The first harmonic is typically the most intense standing wave elicited by physical perturbations of the pipe. Furthermore, higher harmonics have smaller wavelengths and higher frequencies than those of the first harmonic. For a pipe closed at one end, the wavelength of each harmonic is proportional to object length (L) and harmonic number (n = 1, 3, 5…): 11ecba2d_1312_da6b_a3bf_e5d985f28660_MD0008_00 Pipes closed at one end cannot produce even-numbered harmonics (n = 2, 4, 6…), as no displacement of air takes place at the closed end. In other words, the closed end of the pipe is always a node (ie, a point of minimum displacement) and the open end of the pipe is always an antinode (ie, a point of maximum displacement). Nevertheless, even-numbered harmonics retain a place within the harmonic series. Consequently, the harmonic number associated with the second-longest standing wave of a pipe closed at one end is not 2 but 3. In such a case, the expression that gives the wavelength of the third harmonic is: 11ecba2d_1312_da6c_a3bf_610c86d23db2_MD0008_00 Therefore, the expression that gives the wavelength of the third harmonic for a 1.5 m pipe that is closed at one end is: 11ecba2d_1312_da6d_a3bf_5545ddf32355_MD0008_00 Educational objective: Standing waves can be elicited within open and closed pipes. There are no even-numbered harmonics in the harmonic series of a pipe closed at one end because the closed end of a pipe is always a node and the open end is always an antinode.

What Expression Gives the Wavelength of the Third Harmonic for a 1.5