Standing Waves in Strings and Organ Pipes, Fundamental Mode and Harmonics, Beats NEET Questions

Physics - Oscillations and Waves

Standing Waves in Strings and Organ Pipes, Fundamental Mode and Harmonics, Beats MCQ Questions


7.
In a standing wave, particles on OPPOSITE sides of a node are:
A.
Phase difference of Ļ€/2
B.
Exactly in phase
C.
No fixed phase relationship
D.
Exactly out of phase ā€” they always move in opposite directions (phase difference = Ļ€)
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ANSWER :
D. Exactly out of phase ā€” they always move in opposite directions (phase difference = Ļ€)
8.
The energy in a standing wave compared to two constituent progressive waves is:
A.
Half ā€” destructive interference destroys half the energy
B.
Equal ā€” total energy is conserved; energy is redistributed (concentrated near antinodes, zero near nodes) but total is preserved
C.
Zero ā€” standing waves carry no energy
D.
Double ā€” energy is created by constructive interference
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ANSWER :
B. Equal ā€” total energy is conserved; energy is redistributed (concentrated near antinodes, zero near nodes) but total is preserved
9.
A string of length L is fixed at both ends. The boundary conditions require:
A.
No restriction on wavelength ā€” any wavelength is possible
B.
A node at one end and antinode at the other
C.
Nodes at both fixed ends (x = 0 and x = L), so L must equal an integer number of half-wavelengths: L = nĪ»/2
D.
Antinodes at both fixed ends
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ANSWER :
C. Nodes at both fixed ends (x = 0 and x = L), so L must equal an integer number of half-wavelengths: L = nĪ»/2
10.
The allowed wavelengths for standing waves in a string of length L fixed at both ends are:
A.
Any wavelength Ī» such that Ī» < 2L
B.
Ī»_n = 2L/n for n = 1, 2, 3,ā€¦ (wavelength must fit an integer number of half-wavelengths in L)
C.
Ī»_n = 4L/n for n = 1, 2, 3,ā€¦
D.
Ī»_n = 4L/(2nāˆ’1) for n = 1, 2, 3,ā€¦
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ANSWER :
B. Ī»_n = 2L/n for n = 1, 2, 3,ā€¦ (wavelength must fit an integer number of half-wavelengths in L)
11.
The allowed frequencies (normal modes) for a string of length L fixed at both ends with wave speed v are:
A.
Ī½_n = nv/(4L) for n = 1, 2, 3,ā€¦
B.
Ī½_n = (2nāˆ’1)v/(4L) for n = 1, 2, 3,ā€¦ ā€” only ODD harmonics
C.
Ī½_n = nv/(2L) for n = 1, 2, 3,ā€¦ ā€” ALL harmonics (both odd and even)
D.
Only one frequency Ī½ā‚ = v/(2L) is possible
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ANSWER :
C. Ī½_n = nv/(2L) for n = 1, 2, 3,ā€¦ ā€” ALL harmonics (both odd and even)
12.
The FUNDAMENTAL MODE (first harmonic) of a string fixed at both ends has:
A.
Nodes at ends and centre; wavelength Ī»ā‚ = 2L/3
B.
One antinode at each end and node at centre; wavelength Ī»ā‚ = L
C.
One antinode at the centre; two nodes at the ends; wavelength Ī»ā‚ = 2L; frequency Ī½ā‚ = v/(2L)
D.
Two antinodes and one node at the centre; wavelength Ī»ā‚ = L
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ANSWER :
C. One antinode at the centre; two nodes at the ends; wavelength Ī»ā‚ = 2L; frequency Ī½ā‚ = v/(2L)