1. What is the longest wavelength for standing sound waves in a 133.9cm long tube that is open at both ends?
b).What is the second longest wavelength?
c).What is the third longest wavelength?
d).What is the longest wavelength for a standing wave, in the same length tube, that is open at one end and closed at the other?
e). What is the second longest wavelength?
f).What is the third longest wavelength?
To find the longest wavelength for standing sound waves in a tube, you can use the formula:
λ = 2L / n
Where λ is the wavelength, L is the length of the tube, and n is the harmonic number, which represents the number of half-wavelengths that fit in the tube.
a) For the longest wavelength in a tube open at both ends, you can determine the harmonic number that corresponds to the longest wavelength. In this case, it would be n = 1, as the fundamental mode (first harmonic) has one half-wavelength in the tube. Plugging the values into the formula, you get:
λ1 = 2 * 133.9 cm / 1 = 267.8 cm
So, the longest wavelength is 267.8 cm.
b) To find the second longest wavelength, you need to find the harmonic number that corresponds to it. In this case, it would be n = 2, as the second harmonic has two half-wavelengths in the tube. Plugging the values into the formula, you get:
λ2 = 2 * 133.9 cm / 2 = 133.9 cm
So, the second longest wavelength is 133.9 cm.
c) Following the same logic, the third longest wavelength occurs when n = 3, as the third harmonic has three half-wavelengths in the tube. Plugging the values into the formula, you get:
λ3 = 2 * 133.9 cm / 3 ≈ 89.3 cm
So, the third longest wavelength is approximately 89.3 cm.
d) For a tube that is closed at one end and open at the other, the formula changes slightly:
λ = 4L / n
e) Following the same steps as before, the longest wavelength occurs when n = 1, and you can calculate it with the formula:
λ1 = 4 * 133.9 cm / 1 = 535.6 cm
So, the longest wavelength for a tube closed at one end and open at the other is 535.6 cm.
f) The second longest wavelength is n = 3 in this case, and you can calculate it with the formula:
λ2 = 4 * 133.9 cm / 3 ≈ 179.1 cm
So, the second longest wavelength is approximately 179.1 cm.
These calculations provide you with the answers to each question, explaining the steps involved in finding them.