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There are three things to note about the normal modes of a string. 1. m is the number of antinodes on the standing wave, not
the number of nodes. You can tell a string’s mode of oscillation by counting the number of antinodes.
2. The fundamental mode, with m = 1, has λ1 = 2L, not λ1 = L. Only half of a wavelength is contained between the boundaries, a direct consequence of the fact that the spacing between nodes is λ/2.
3. The frequencies of the normal modes form a series: f1, 2f1, 3f1, …The fundamental frequency f1 can be found as the difference between the frequencies of any two adjacent modes. That is, f1 = Δf = fm+1 – fm.
A standing wave on a string vibrates as shown at the top. Suppose the tension is quadrupled while the frequency and the length of the string are held constant. Which standing wave pattern is produced?
A standing wave on a string vibrates as shown at the top. Suppose the tension is quadrupled while the frequency and the length of the string are held constant. Which standing wave pattern is produced?
An open-open tube of air supports standing waves at frequencies of 300 Hz and 400 Hz, and at no frequencies between these two. The second harmonic of this tube has frequency A. 800 Hz. B. 200 Hz. C. 600 Hz. D. 400 Hz. E. 100 Hz.
An open-open tube of air supports standing waves at frequencies of 300 Hz and 400 Hz, and at no frequencies between these two. The second harmonic of this tube has frequency
A. 800 Hz. B. 200 Hz. C. 600 Hz. D. 400 Hz. E. 100 Hz.
Interference in One Dimension The pattern resulting from the superposition of two waves is often called interference. In this section we will look at the interference of two waves traveling in the same direction.
Two speakers are emitting identical sound waves with a wavelength of 4.0 m. The speakers are 8.0 m apart, directed toward each other, as in the diagram below.
Checking Understanding: Interference Along a Line
At each of the noted points in the above diagram, is the interference
A. constructive? B. destructive? C. something in between?
Two speakers are emitting identical sound waves with a wavelength of 4.0 m. The speakers are 8.0 m apart, directed toward each other, as in the diagram below.
Answer
Slide 16-21
At each of the noted points in the above diagram, is the interference
A. constructive? (a), (c), (e) B. destructive? (b), (d) C. something in between?