Calculating 2nd and 3rd Resonant Lengths

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The first resonant length of a closed air column is 30.0 cm, leading to calculations for the second and third resonant lengths. The second resonant length is determined to be 90.0 cm, and the third is 150.0 cm, based on the relationship of multiples of the fundamental frequency. The wavelength is calculated as 120 cm, with the second resonant length corresponding to three-quarters of a wavelength. Understanding the positioning of nodes and antinodes is crucial for these calculations. The discussion emphasizes the importance of correctly applying the quarter wavelength principle in resonant length calculations.
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Homework Statement


The 1st rensonat length of a closed air column occurs when the length is 30.0cm. what will the send ond and third be?

Homework Equations


I did the pattern thign like 3/4 but i got the wrong answer.

The Attempt at a Solution



i multplied the legth 3/4 but i got the wrong answer.
 
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Second = 30.0*3=90.0 (cm)
Third= 30.0*5 = 150.0(cm)
u can draw graphs to know why.
 
A node is situated at the closed end an antinode at the open end. The "smallest structure" of the wavelenght that can accommodate this is a quarter wavelength.Which means that the wavelength is 120 cm. The next waveform will be three quarters of a wavelength (again a node at the closed end and an antinode at the open end).
 

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