Transverse Waves on a Stretched String and Wave Speed questions with solutions

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• MCQmediumWave MotionTransverse Waves on a Stretched String and Wave Speed

  A sinusoidal transverse wave y = A sin(kx-ωt) travels along a string of linear mass density μ with wave speed v. Which expression gives the average rate P̄ at which energy is transported past a fixed point of the string?

  Options

  • Option A

    P̄ = μω²A²v

  • Option B

    P̄ = ½μω²A²v

  • Option C

    P̄ = ½μωA²v²

  • Option D

    P̄ = ½μA²v

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• NumericeasyWave MotionTransverse Waves on a Stretched String and Wave Speed

  A travelling wave on a string carries an average power of 12 W and has frequency 4 Hz. If the energy transported through a fixed point during one complete time period is N joules, find N.

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• MCQeasyWave MotionTransverse Waves on a Stretched String and Wave Speed

  A steel wire with mass per unit length 7.0 × 10⁻³ kg m⁻¹ is under tension of 70 N. The speed of transverse waves in the wire will be:

  Options

  • Option A

    200π m s⁻¹

  • Option B

    100 m s⁻¹

  • Option C

    10 m s⁻¹

  • Option D

    50 m s⁻¹

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• NumericmediumWave MotionTransverse Waves on a Stretched String and Wave Speed

  A sinusoidal wave travels along a string with linear density 0.02 kg/m, amplitude 0.02 m, angular frequency 100 rad/s and wave speed 50 m/s. If its average power is N watts, find N.

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• MCQmediumWave MotionTransverse Waves on a Stretched String and Wave Speed

  Two uniform strings are made of the same material and are maintained under the same tension. Their radii are r and 2r. If the corresponding transverse wave speeds are v₁ and v₂, what is the ratio v₁/v₂?

  Options

  • Option A

    1/2

  • Option B

    2

  • Option C

    4

  • Option D

    1

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• NumericeasyWave MotionTransverse Waves on a Stretched String and Wave Speed

  The tension in a uniform string is increased from T to 9T while the linear mass density remains unchanged. If the initial wave speed is v and the new wave speed is Nv, find N.

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• MCQmediumWave MotionTransverse Waves on a Stretched String and Wave Speed

  Two strings (A, B) having linear densities $\mu_{A}$ = 2 × 10⁻⁴ kg·m⁻¹ and $\mu_{B}$= 4 × 10⁻⁴ kg·m⁻¹ and lengths L₍ᴀ₎ = 2.5 m and L₍ʙ₎ = 1.5 m respectively are joined. Free ends of A and B are tied to two rigid supports C and D, respectively creating a tension of 500 N in the wire. Two identical pulses, sent from C and D ends, take time t₁ and t₂, respectively, to reach the joint. The ratio t₁ ─── t₂ is :

  Options

  • Option A

    1.08

  • Option B

    1.90

  • Option C

    1.67

  • Option D

    1.18

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• MCQeasyWave MotionTransverse Waves on a Stretched String and Wave Speed

  A stretched string has tension T and linear density μ. A vibrator of fixed frequency f generates a sinusoidal transverse wave on the string. Which expression gives the wavelength λ?

  Options

  • Option A

    f√(T/μ)

  • Option B

    (1/f)√(T/μ)

  • Option C

    f√(μ/T)

  • Option D

    T/(μf)

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• MCQeasyWave MotionTransverse Waves on a Stretched String and Wave Speed

  Two strings of the same material and under the same tension have circular radii R and R/2. If transverse wave speeds are v₁ and v₂ respectively, the ratio v₂/v₁ is:

  Options

  • Option A

    √2

  • Option B

    2

  • Option C

    8

  • Option D

    4

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• MCQeasyWave MotionTransverse Waves on a Stretched String and Wave Speed

  A transverse wave propagates on an ideal stretched string having tension T and linear mass density μ. Which expression gives the wave speed?

  Options

  • Option A

    √(μ/T)

  • Option B

    √(T/μ)

  • Option C

    T/μ

  • Option D

    √(Tμ)

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