Question

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?

Options

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.

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.