The third resonant length of a closed air column is 75cm . What is the first and second length
L= 5•λ/4,
λ =4•L/5 = 4•75/5= 60,
L1 = λ/4 =60/4=15 cm,
L2=3•λ/4=45 cm.
The third resonant length of a closed air column (open at one end and closed at the other end) is 75 cm. Determine the first and second resonant lengths.
Well, if the third resonant length is 75 cm, then we can assume that the first and second lengths are taking some time off to relax at the beach. They must be enjoying themselves so much that they forgot to show up! Maybe they'll join the party later, or maybe they just wanted to let the third length have its moment in the spotlight. Who knows, lengths can be quite mysterious sometimes!
To find the first and second resonant lengths of a closed air column, we can use the formula:
L = (2n - 1) * (v/4f)
where:
L is the length of the air column
n is the harmonic number (1 for the first, 2 for the second, etc.)
v is the speed of sound in air (approximately 343 m/s)
f is the frequency of the sound wave
Given that the third resonant length of the air column is 75 cm (or 0.75 m), we can calculate the first and second lengths as follows:
For the third resonant length (n = 3):
0.75 = (2 * 3 - 1) * (343 / (4 * f))
Simplifying the equation:
0.75 = 5 * 343 / (4 * f)
0.75 * 4 * f = 5 * 343
3 * f = (5 * 343) / 4
f = (5 * 343) / (4 * 3)
f = 57.17 Hz
Now that we have the frequency, we can find the first and second resonant lengths:
For the first resonant length (n = 1):
L1 = (2 * 1 - 1) * (343 / (4 * 57.17))
L1 = 171.5 cm (or 1.715 m)
For the second resonant length (n = 2):
L2 = (2 * 2 - 1) * (343 / (4 * 57.17))
L2 = 514.5 cm (or 5.145 m)
Therefore, the first resonant length is approximately 1.715 m and the second resonant length is approximately 5.145 m.
To find the first and second resonant lengths of a closed air column, we need to know the formula for calculating the resonant lengths.
The formula for the resonant lengths of a closed air column is given by:
Ln = (2n - 1) * (v/4f),
where Ln represents the nth resonant length, n is the order of the resonant length, v is the speed of sound in air, and f is the frequency of the sound wave.
However, in this case, we are given the third resonant length (L3 = 75 cm). We can use this information to find the values of the first (L1) and second (L2) resonant lengths.
To find L1, we use the formula:
L1 = (L3 * f3) / f1,
where f3 and f1 represent the frequencies corresponding to the third and first resonant lengths, respectively.
To find L2, we use the formula:
L2 = (L3 * f3) / f2,
where f2 represents the frequency corresponding to the second resonant length.
Given that we don't have any information about the frequencies f1, f2, and f3, we cannot directly calculate the first and second resonant lengths. We need more information to proceed with the calculations.