Physics · Wave Motion and Sound
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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?
- A
0.20 m
- B
0.40 m
- C
0.80 m
- D
1.60 m
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.
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.
Understanding Harmonics in Open Tubes
- In a tube open at both ends, the second harmonic corresponds to a standing wave pattern with a full wavelength fitting within the tube's length. There are antinodes (points of maximum displacement) at both ends, and a node (point of zero displacement) in the middle.
Relationship between Wavelength and Tube Length
For the second harmonic in an open tube:
Wavelength (λ) = Length of the tube (L)
Calculation
Given that the length of the tube is 0.80 m:
λ = 0.80 m
Answer:
The wavelength of the waves that make up the standing wave is 0.80 meters.
Option D is incorrect since it states 1.60m which corresponds to double wavelength.
Tagged under Physics · Wave Motion and Sound