A longitudinal standing wave, in second harmonic mode, is established in a tube that is open at both ends. The length of the tube is 0.80m. What is the wavelength of the waves that make up the standing wave?
Correct answer: C. 0.80m
- A. 0.20 m
- B. 0.40 m
- C. 0.80m
- D. 1.60m
Explanation
Option C is correct since according to the formula for standing waves in an open pipe, the fundamental frequency is : v/2L. For the second harmonic, the frequency is 2v/2L. Let's calculate the wavelength of the waves according to the formula given in the image.As the length of the tube is 0.80m, there will be three antinodes and 2 nodes. Since L= (2 * lambda )/2, so L= lambda. So 0.80m is the wavelength of the waves.Option A is incorrect since it states 0.20m which corresponds to a quarter of a wavelength.Option B is incorrect since it states 0.40m which corresponds to half a wavelength.Option D is incorrect since it states 1.60m which corresponds to double wavelength.
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About Stationary Waves
Stationary waves form when two waves of the same frequency and amplitude travel in opposite directions and interfere. The topic covers nodes, antinodes, wavelength, phase, resonance, and the allowed frequencies on strings and in air columns. Unlike progressive waves, stationary waves do not transfer energy from one point to another.
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