A steel tube, which is closed at both ends, is filled with air. The air in the tube is vibrating at a frequency of 200·Hz. Use 340·m/s for the speed of sound in air.
(a) What is the wavelength of the sound waves in the tube? m.
(b) If the 200·Hz vibration respresents the fundamental standing wave for the tube, how long is the tube? m.
(c) If the air in the tube is replaced with a different gas, the frequency of the fundamental standing wave changes to 160·Hz. What is the speed of sound in this new gas? m/s.
a. WL = V/f = 340/200 Meters.
b. L = WL = V/f = 340/200 meters.
Can Damon answer this
What equations can I use to solve?
To answer these questions, we need to understand the concept of a closed-end tube and standing waves.
(a) The wavelength of a sound wave can be calculated using the formula:
Wavelength = Speed of Sound / Frequency
Substituting the given values:
Speed of Sound = 340 m/s
Frequency = 200 Hz
Wavelength = 340 m/s / 200 Hz
Therefore, the wavelength of the sound waves in the tube is 1.7 m.
(b) In a closed-end tube, the fundamental frequency is created when the wavelength is 2 times the length of the tube. For a tube closed at both ends:
Fundamental Frequency = (Speed of Sound) / (2 * Length)
We are given that the fundamental frequency is 200 Hz.
200 Hz = 340 m/s / (2 * Length)
Solving for Length:
Length = 340 m/s / (2 * 200 Hz)
Therefore, the length of the tube is 0.85 m.
(c) If the frequency of the fundamental standing wave changes to 160 Hz, we can calculate the speed of sound in the new gas using the same formula as before.
Speed of Sound in new gas = Frequency * Wavelength
Substituting the given values:
Frequency = 160 Hz
Wavelength (from part a) = 1.7 m
Speed of Sound in new gas = 160 Hz * 1.7 m
Therefore, the speed of sound in the new gas is 272 m/s.