stationary wave of string and sonometer questions with solutions

Showing 1–10 of 27 questions

• NumericeasyWave Motionstationary wave of string and sonometer

  A stretched string fixed at both ends vibrates in its fifth harmonic. If the total number of displacement nodes, including the two fixed ends, is N, find N.

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• NumericeasyWave Motionstationary wave of string and sonometer

  A stationary wave on a string has wavelength 0.80 m. If the distance between two consecutive displacement nodes is N cm, find N.

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• MCQmediumWave Motionstationary wave of string and sonometer

  A string of length L is fixed at one end and perfectly free at the other end. Transverse waves on the string have speed v. Which expression gives the allowed natural frequencies?

  Options

  • Option A

    fₙ = nv/(2L)

  • Option B

    fₙ = (2n-1)v/(4L)

  • Option C

    fₙ = nv/(4L)

  • Option D

    fₙ = (2n+1)v/(2L)

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• MCQmediumWave Motionstationary wave of string and sonometer

  A sonometer wire resonates in its fundamental mode at frequency f. The vibrating length is then doubled without changing the wire. By what factor must the tension be changed so that the fundamental frequency remains unchanged?

  Options

  • Option A

    2

  • Option B

    4

  • Option C

    1/2

  • Option D

    1/4

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• IntegermediumWave Motionstationary wave of string and sonometer

  A wire of density 8 × 10³ kg m⁻³ is stretched between clamps 0.5 m apart. Its extension is 3.2 × 10⁻⁴ m. If Y = 8 × 10¹⁰ N m⁻², find its fundamental frequency in Hz.

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  JEE Mains11 April 2023Shift 2Evening Shift

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• NumericmediumWave Motionstationary wave of string and sonometer

  A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be __________ cm.

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  JEE Mains8 April 2023Shift 2Evening Shift

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• Multi-correctmediumWave Motionstationary wave of string and sonometer

  Which statements are correct for an ideal stationary transverse wave on a string?

  Select all that apply

  • Option A

    Displacement nodes remain permanently at zero displacement.

  • Option B

    Antinodes have the maximum displacement amplitude.

  • Option C

    Adjacent displacement nodes are separated by λ/2.

  • Option D

    There is no net average energy transport along the string.

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• MCQeasyWave Motionstationary wave of string and sonometer

  A stretched string fixed at both ends vibrates in its nth harmonic. How many displacement nodes and antinodes are present, including the two fixed ends as nodes?

  Options

  • Option A

    n nodes and n+1 antinodes

  • Option B

    n+1 nodes and n antinodes

  • Option C

    2n nodes and n antinodes

  • Option D

    n nodes and 2n antinodes

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• Multi-correctmediumWave Motionstationary wave of string and sonometer

  A uniform string of length L is fixed at both ends and supports stationary transverse waves. Which statements are correct for its nth harmonic?

  Select all that apply

  • Option A

    λₙ = 2L/n

  • Option B

    fₙ = nv/(2L)

  • Option C

    The nth harmonic contains n antinodes.

  • Option D

    The nth harmonic contains n+1 nodes including the fixed ends.

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• Multi-correctmediumWave Motionstationary wave of string and sonometer

  Which statements are correct about the phase and amplitude of particles in an ideal stationary wave on a string?

  Select all that apply

  • Option A

    All particles between the same pair of adjacent nodes oscillate in the same phase.

  • Option B

    Particles in two adjacent loops oscillate in opposite phase.

  • Option C

    A displacement node has zero oscillation amplitude.

  • Option D

    If each component travelling wave has amplitude A, a displacement antinode has amplitude 2A.

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