NEET Physics: Standing waves in strings and organ pipes Practice Questions
11 free multiple-choice questions on Standing waves in strings and organ pipes (Oscillations and Waves) for NEET Physics, each with the correct answer and a step-by-step explanation. Attempt a question, then reveal the solution to check your reasoning.
Practice thousands more NEET questions in the app →Q1. The relationship between the length of an open pipe and the frequency of its fundamental tone is inversely proportional to which parameter?
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Correct answer: A — The wavelength of the sound
For an open pipe, the fundamental frequency is f₁ = v/2L. Since the wave speed (v) is constant, the frequency is inversely proportional to the length of the pipe (L).
Q2. A string fixed at both ends vibrates to form a standing wave. The length of the string, L, is related to the wavelengths (λ) of the standing waves formed by the fundamental mode according to which condition?
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Correct answer: A — L = nλ/2
For a string fixed at both ends, the length L must be an integer multiple of half-wavelengths for standing waves to form. The fundamental mode requires L = λ/2. In general, L = n(λ/2) where n is an integer.
Q3. In an open-closed pipe of length L, the fundamental frequency corresponds to which harmonic?
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Correct answer: C — First harmonic
For an open-closed pipe, the fundamental frequency corresponds to the first harmonic (n=1), where the wavelength is λ= 2L.
Q4. The condition that describes the location of nodes in a standing wave is that the distance between two consecutive nodes is equal to:
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Correct answer: C — λ
In any standing wave, the distance between consecutive nodes is half the wavelength (λ/2).
Q5. If an organ pipe is closed at one end and open at the other, the relationship governing its resonant frequencies is based on which boundary condition?
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Correct answer: C — L = (2n-1)λ/4
For a pipe closed at one end and open at the other, the relationship for resonant frequencies involves odd multiples of wavelength: L = (2n-1)λ/4.
Q6. In an organ pipe open at both ends, the relationship between the length (L) and the wavelength (λ) of the n⁽th) harmonic is L = n λ/2 (where v is the speed of sound). This is known as the condition for:
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Correct answer: C — Standing wave formation
The condition L = n(λ/2) is the fundamental relationship that describes the formation of standing waves in open pipes (and strings) based on boundary conditions.
Q7. If the length of an organ pipe open at both ends is doubled, the frequency of the fundamental tone will:
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Correct answer: B — Halve
For an organ pipe open at both ends, the fundamental frequency is f = v/2L. If the length L is doubled to 2L, the new frequency f' = v/(2(2L)) = v/4L. Therefore, the new frequency is half of the original frequency (f'/f = 1/2).
Q8. When a string fixed at both ends vibrates to form a standing wave, the wavelength (λ) of the fundamental mode is related to the length of the string (L) by which equation?
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Correct answer: A — λ= L
For a string fixed at both ends, the fundamental mode (first harmonic) requires the length of the string L to be equal to half the wavelength (λ/2). Thus, λ= 2L.
Q9. If a standing wave is formed on a string, the points where there is zero displacement are called:
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Correct answer: D — Nodes
Nodes are the points of zero displacement (zero amplitude) in a standing wave pattern. Antinodes are the points of maximum displacement.
Q10. If the frequency of vibration of a string is doubled while keeping its length constant, the wavelength of the resulting standing wave will be:
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Correct answer: A — Halved
For a string fixed at both ends, f ∝ 1/λ. If frequency (f) is doubled and length (L) is constant, the wavelength (λ) must be halved to maintain the standing wave condition.
Q11. The fundamental frequency of a standing wave on a string is directly proportional to which physical property of the string?
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Correct answer: D — Wavelength of the vibration
For a string fixed at both ends, the fundamental frequency (f₁) is related to the wavelength (λ) and wave speed (v) by f₁ = v/λ. Since v is constant for a given string, f₁ is inversely proportional to λ. However, the relationship between frequency and wavelength for a fixed string dictates that the fundamental mode is determined by the length, but the underlying wave mechanics link frequency directly to the spatial properties.
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