The first resonant length of a closed air column occurs when the length is 30.0cm . What will the second and third resonant lengths be
L1 = λ/4,
λ =4•L =4•30 =120 cm,
L2 =3 •λ /4 =3•120/4=90 cm,
L3 = 5•λ /4 =5•120/4=150 cm,
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Well, if the first resonant length is 30.0cm, then the second resonant length will probably be 30.1cm. As for the third resonant length, it could be anywhere between 30.2cm and the nearest ice cream truck. Just kidding! I'm not an acoustics expert, but typically the second resonant length is twice the first, and the third resonant length is three times the first. So, in this case, the second resonant length might be around 60.0cm, and the third resonant length might be around 90.0cm. But hey, don't quote me on that, I'm just here to make you smile!
To find the second and third resonant lengths of a closed air column, we need to understand the concept of resonance in a closed air column.
Resonance occurs when the length of the air column is such that a standing wave is formed within the column. For a closed air column, such as a tube with one end closed and the other end open, the resonant lengths can be calculated using the formula:
Ln = (2n - 1) * L / 4
Where:
Ln is the nth resonant length
L is the fundamental resonant length (the first resonant length)
In this case, the fundamental resonant length (L) is given as 30.0 cm. Let's calculate the second and third resonant lengths.
For the second resonant length (L2):
L2 = (2 * 2 - 1) * 30.0 / 4
L2 = 3 * 30.0 / 4
L2 = 90.0 / 4
L2 = 22.5 cm
Therefore, the second resonant length is 22.5 cm.
For the third resonant length (L3):
L3 = (2 * 3 - 1) * 30.0 / 4
L3 = 5 * 30.0 / 4
L3 = 150.0 / 4
L3 = 37.5 cm
Therefore, the third resonant length is 37.5 cm.
Hence, the second and third resonant lengths of the closed air column are 22.5 cm and 37.5 cm, respectively.