Transverse Stationary Waves and Sonometer PYQs: JEE Mains Physics

Showing 1–19 of 19 questions

1. 1. The equation of a wave travelling on a string is \(\mathrm{y}=\sin [20 \pi \mathrm{x}+10 \pi \mathrm{t}]\), where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is : 2025 Easy
2. 2. A sonometer wire of resonating length \(90 \mathrm{~cm}\) has a fundamental frequency of \(400 \mathrm{~Hz}\) when kept under some tension. The resonating length of the wire with fundamental frequency of \(600 \mathrm{~Hz}\) under same tension ________ \(\mathrm{cm}\). 2024 Hard
3. 3. 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 \(...........cm\). 2023 Easy
4. 4. A wire of density \(8 \times 10^3\,kg / m ^3\) is stretched between two clamps \(0.5\,m\) apart. The extension developed in the wire is \(3.2 \times 10^{-4}\,m\). If \(Y =8 \times 10^{10}\,N / m ^2\), the fundamental frequency of vibration in the wire will be \(......\,Hz\). 2023 Medium
5. 5. In an experiment with sonometer when a mass of \(180\,g\) is attached to the string, it vibrates with fundamental frequency of \(30\,Hz\). When a mass \(m\) is attached, the string vibrates with fundamental frequency of \(50\,Hz\). The value of \(m\) is \(.........\,g\). 2023 Easy
6. 6. The fundamental frequency of vibration of a string stretched between two rigid support is \(50\,Hz\). The mass of the string is \(18\,g\) and its linear mass density is \(20\,g / m\). The speed of the transverse waves so produced in the string is \(..........\,ms ^{-1}\) 2023 Medium
7. 7. A wire of length \(30\,cm\), stretched between rigid supports, has it's \(n^{\text {th}}\) and \((n+1)^{\text {th}}\) harmonics at \(400\,Hz\) and \(450\; Hz\), respectively. If tension in the string is \(2700\,N\), it's linear mass density is.........\(kg/m\). 2022 Easy
8. 8. A wire having a linear mass density \(9.0 \times 10^{-4} \;{kg} / {m}\) is stretched between two rigid supports with a tension of \(900\; {N}\). The wire resonates at a frequency of \(500\;{Hz}\). The next higher frequency at which the same wire resonates is \(550\; {Hz}\). The length of the wire is \(...... {m}\) 2021 Hard
9. 9. A wire of length \(L\) and mass per unit length \(6.0\times 10^{-3}\; \mathrm{kgm}^{-1}\) is put under tension of \(540\; \mathrm{N}\). Two consecutive frequencies that it resonates at are : \(420\; \mathrm{Hz}\) and \(490 \;\mathrm{Hz}\). Then \(\mathrm{L}\) in meters is 2020 Easy
10. 10. For a transverse wave travelling along a straight line, the distance between two peaks (crests) is \(5 \,m ,\) while the distance between one crest and one trough is \(1.5 \,m\) The possible wavelengths (in \(m\) ) of the waves are 2020 Easy
11. 11. Two identical strings \(X\) and \(Z\) made of same material have tension \(T _{ x }\) and \(T _{ z }\) in them. If their fundamental frequencies are \(450\, Hz\) and \(300\, Hz ,\) respectively, then the ratio \(T _{ x } / T _{ z }\) is\(.....\) 2020 Easy
12. 12. A string \(2.0\, m\) long and fixed at its end is driven by a \(240\, Hz\) vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is 2019 Easy
13. 13. A string is clamed at both the ends and it is vibrating in its \(4^{th}\) harmonic. The equation of the stationary wave is \(Y =0.3\,sin\,(0.157\,x) \,cos\,(200\pi t)\). The length of the string is ..... \(m\) (all quantities are in \(SI\) units) 2019 Easy
14. 14. A string of length \(1\, m\) and mass \(5\, g\) is fixed at both ends. The tension in the string is \(8.0\, N\). The string is set into vibration using an external vibrator of frequency \(100\, Hz\). The separation between successive nodes on the string is close to .... \(cm\) 2019 Medium
15. 15. A wire of length \(2\,L\) is made by joining two wires \(A\) and \(B\) of same lengths but different radii \(r\) and \(2r\) and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire \(A\) is \(p\) and that in \(B\) is \(q\) then the ratio \(p : q\) is
    2019 Hard
16. 16. Two wires \(W_1\) and \(W_2\) have the same radius \(r\) and respective densities \({\rho _1}\) and \({\rho _2}\) such that \({\rho _2} = 4{\rho _1}\). They are joined together at the point \(O\), as  shown in the figure. The combination is used as a sonometer wire and kept under tension \(T\). The point \(O\) is midway between the two bridges. When a stationary waves is set up in the composite wire, the joint is found to be a node. The ratio of the number of an tin odes formed in \(W_1\) to \(W_2\) is
    2017 Medium
17. 17. The total length of a sonometer wire between fixed ends is \(110\, cm\). Two bridges are placed to divide the length of wire in ratio \(6 : 3 : 2\). The tension in the wire is \(400\, N\) and the mass per unit length is \(0.01\, kg/m\) . What is the minimum common frequency with Which three parts can vibrate ........... \(Hz\) ? 2014 Medium
18. 18. A sonometer wire of length \(114\, cm\) is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio \(1 : 3 : 4\) ? 2013 Hard
19. 19. A sonometer wire oflength \(1.5\ m\) is made of steel. The tension in it produces an elastic strain of \(1 \%\). What is the fundamental frequency of steel if density and elasticity of steel are \(7.7 \times 10^3 \) \(kg/m^3\) and \(2.2 \times 10^{11}\) \(N/m^2\) respectively? 2013 Easy

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