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question based on string wave questions with solutions

Practice Wave Motion for JEE Main, JEE Advanced, NEET, and Classes 11–12. Attempt each question, then open it for the full solution.

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MCQmediumWave Motion
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?
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MCQmediumWave Motion
A wave travelling on a string is y = sin(20πx + 10πt), with x and t in SI units. The minimum distance between two points having the same oscillating speed is:
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JEE Mains 2025 7 April Evening Shift
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MCQeasyWave Motion
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?
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MCQmediumWave Motion
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 :
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NumericeasyWave Motion
A transverse wave travels along a string with speed 40 m/s. The string has linear mass density 0.025 kg/m. If the tension in the string is N newtons, find N.
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NumericeasyWave Motion
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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MCQeasyWave Motion
A transverse wave propagates on an ideal stretched string having tension T and linear mass density μ. Which expression gives the wave speed?
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NumericmediumWave Motion
Two stretched strings are maintained under the same tension. Their transverse wave speeds are 60 m/s and 30 m/s. If their linear densities are μ₁ and μ₂ respectively and μ₂/μ₁ = N, find N.
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NumericmediumWave Motion
A horizontal string of linear density 0.01 kg/m is stretched by a hanging mass of 10 kg over a smooth pulley. A vibrator of frequency 50 Hz produces transverse waves on the horizontal part of the string. Take g = 10 m/s². If the wavelength is N/5 metres, find N.
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MCQmediumWave Motion
A sinusoidal wave on a given stretched string has amplitude A, frequency f and average power P̄. The amplitude is doubled while the frequency is reduced to one-half. The string tension and linear density remain unchanged. What is the new average power?
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