OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(g) fundamental mode of vibration (1st harmonic); harmonics.
Full specification wording
Stationary waves: (g) fundamental mode of vibration (1st harmonic); harmonics.
A stationary wave on a stretched string or in a pipe can vibrate in several distinct patterns called harmonics.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 8 of 8
- 2 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A stationary wave on a stretched string or in a pipe can vibrate in several distinct patterns called harmonics. The simplest pattern is the fundamental mode, also called the first harmonic. For a string fixed at both ends, the fundamental has one antinode in the middle and nodes at each end, so the string length L equals λ/2. The second harmonic has two antinodes and L = λ, the third harmonic has three antinodes and L = 3λ/2, and so on. In general, for a string fixed at both ends, L = nλ/2 where n is the harmonic number. The frequency of each harmonic is an integer multiple of the fundamental frequency: f_n = nf_1. For a pipe open at both ends, the pattern is similar, but a pipe closed at one end has only odd harmonics.
What earns the marks
- Defines the fundamental mode (first harmonic) as the lowest frequency stationary wave pattern.
- States that for a string fixed at both ends, the fundamental has L = λ/2.
- Identifies that the nth harmonic has n antinodes and L = nλ/2 for a string fixed at both ends.
- States that harmonic frequencies are integer multiples of the fundamental frequency.
- Recognises that a pipe closed at one end supports only odd harmonics.
Common mistakes and how to put them right
Confusing the harmonic number with the number of nodes.
Put it right: The nth harmonic has n antinodes and n+1 nodes for a string fixed at both ends.
Assuming that a closed pipe supports all harmonics.
Put it right: It supports only odd harmonics.
Using L = λ for the fundamental of a string fixed at both ends instead of L = λ/2.
Forgetting that the fundamental frequency is the lowest possible frequency, not the highest.
Exam tips
- Count antinodes to identify the harmonic number quickly in diagram questions.
- Write the general relationship L = nλ/2 and rearrange before substituting numbers.
- For closed pipes, remember the sequence 1st, 3rd, 5th harmonic and use odd values of n.
- Check whether the question asks for frequency, wavelength or harmonic number and give the correct quantity with units.
Try the lesson
The start of the Stationary waves: (g) fundamental mode of vibration (1st harmonic); harmonics. lesson, made from checked teaching notes for this specification point.
Listen
A stationary wave on a stretched string or in a pipe can vibrate in several distinct patterns called harmonics. The simplest pattern is the fundamental mode, also called the first harmonic. For a string fixed at both ends, the fundamental has one antinode in the middle and nodes at each end, so the string length L equals λ/2. The second harmonic has two antinodes and L = λ, the third harmonic has three antinodes and L = 3λ/2, and so on. In general, for a string fixed at both ends, L = nλ/2 where n is the harmonic number. The frequency of each harmonic is an integer multiple of the fundamental frequency: f_n = nf_1. For a pipe open at both ends, the pattern is similar, but a pipe closed at one end has only odd harmonics. A strong answer earns marks for these points. Defines the fundamental mode (first harmonic) as the lowest frequency stationary wave pattern. States that for a string fixed at both ends, the fundamental has L = λ/2. Identifies that the nth harmonic has n antinodes and L = nλ/2 for a string fixed at both ends. States that harmonic frequencies are integer multiples of the fundamental frequency. Exam tip: Count antinodes to identify the harmonic number quickly in diagram questions.
See it
Key words
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Fundamental mode
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Harmonics
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See every definition
- Fundamental mode
- The lowest frequency stationary wave pattern, also called the first harmonic.
- Harmonics
- Distinct patterns in which a stationary wave on a stretched string or in a pipe can vibrate, with frequencies that are integer multiples of the fundamental frequency.
Label the diagram
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