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Standing Waves in Strings for JEE: 27 solved questions

Real JEE paper questions on standing waves in strings, part of waves. Each opens with the options, the correct answer and a step-by-step solution. Papers run from 2002 to 2024. No sign-in needed to read them.

What this topic asks

• Nodes, antinodes and harmonics — 17 questions
• Sonometer — 6 questions
• Joined wires and clamped rods — 4 questions

All 27 questions with solutions

• In a sonometer experiment a mass of 180 g attached to the string makes it vibrate at a fundamental frequency… JEE Main 13th April 2nd Shift 2023
• A wire of density 9×10⁻³ kg cm⁻³ is stretched between two clamps 1 m apart, producing a strain of 4.9×10⁻⁴ in… JEE Main 2nd Sept 2nd Shift 2020
• Two identical strings X and Z of the same material are under tensions T_X and T_Z. If their fundamental frequ… JEE Main 2nd Sept 1st Shift 2020
• A wire of length 2L is made by joining two wires A and B of the same length and material but of radii r and 2… JEE Main 8th April 1st Shift 2019
• A string clamped at both ends vibrates in its fourth harmonic, the stationary wave being Y=0.3 sin(0.157x)cos… JEE Main 9th April 1st Shift 2019
• A string 2.0 m long, fixed at both ends, is driven by a 240 Hz vibrator and vibrates in its third harmonic mo… JEE Main 9th April 2nd Shift 2019
• A wire of length L and mass per unit length 6.0×10⁻³ kg m⁻¹ is under a tension of 540 N. Two consecutive reso… JEE Main 9th Jan 2nd Shift 2019
• A string of length 1 m and mass 5 g is fixed at both ends under a tension of 8.0 N, and is driven by an exter… JEE Main 10th Jan 1st Shift 2019
• A granite rod 60 cm long is clamped at its middle point and set into longitudinal vibrations. The density of… JEE Main 2018
• [Figure: two wires W₁ and W₂ of equal radius joined at a point O midway between the two bridges of a sonomete… JEE Main Online 2017
• A standing wave formed by two waves travelling in opposite directions has transverse displacement y(x,t)=0.5… JEE Main Online 2017
• A sonometer wire 1.5 m long is made of steel, and the tension in it produces an elastic strain of 1%. The fun… JEE Main 2013
• A sonometer wire 114 cm long is fixed at both ends. Where should the two bridges be placed to divide the wire… JEE Main Online 2013
• A travelling wave y=A sin(ω t-kx) is superposed on y=A sin(ω t+kx). The resultant is JEE Main Re-Scheduled 2011
• A string is stretched between fixed points 75 cm apart. It has resonant frequencies of 420 Hz and 315 Hz, wit… JEE Main 2006
• A metal wire of linear mass density 9.8 g m⁻¹ is stretched with a tension of 10 kg-wt between rigid supports… JEE Main 2003
• When the temperature increases, the frequency of a tuning fork JEE Main 2002
• A string tied to two rigid supports is 40 cm long. The maximum wavelength of a stationary wave produced on it… JEE Main 2002
• A wave y=a sin(ω t-kx) on a string meets another wave that produces a node at x=0. The equation of the unknow… JEE Main 2002
• A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz under a certain tension. Un… JEE Main 5th April 2nd Shift 2024
• A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of string giving… JEE Main 8th April 2nd Shift 2023
• A wire of density 8×10³ kg m⁻³ is stretched between two clamps 0.5 m apart, the extension developed in the wi… JEE Main 11th April 2nd Shift 2023
• The fundamental frequency of a string stretched between two rigid supports is 50 Hz. The mass of the string i… JEE Main 15th April 1st Shift 2023
• A wire 30 cm long, stretched between rigid supports, has its nth and (n+1)th harmonics at 400 Hz and 450 Hz.… JEE Main 27th July 2nd Shift 2022
• Two travelling waves of equal amplitude and frequency move in opposite directions along a string and form the… JEE Main 24th June 2nd Shift 2022
• A standing wave produced by two travelling waves is y=(1.0 mm)cos (1.57 cm⁻¹ x)sin (78.5 s⁻¹ t). The node clo… JEE Main 26th Aug 1st Shift 2021
• A wire of linear mass density 9.0×10⁻⁴ kg m⁻¹ is stretched between two rigid supports under a tension of 900… JEE Main 31st Aug 1st Shift 2021