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 0.80 m. What is the wavelength of the waves that make up the standing wave?
Correct answer: C. 0.80 m
- A. 0.20 m
- B. 0.40 m
- C. 0.80 m
- D. 1.60 m
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 Waves
Progressive waves transfer energy through oscillations, with wavelength, frequency, amplitude and wave speed related by v = fλ; sound speed depends on the medium. Superposition produces interference and stationary waves in strings and organ pipes, while simple harmonic motion describes the oscillation itself and must be distinguished from wave propagation.
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