Speed of Mechanical Wave on String PYQs: JEE Mains Physics

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1. 1. Two strings (A, B) having linear densities \(\mu_{ A }=2 \times 10^{-4} kg / m\) and \(\mu_{ B }=4 \times 10^{-4} kg / m\) and lengths \(L _{ A }=2.5 m\) and \(L _{ B }=1.5 m\) 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 \(t_1\) and \(t_2\), respectively, to reach the joint. The ratio \(t_1 / t_2\) is : 2026 Medium
2. 2. Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is \(\mathrm{v}_1\), and that in the other string having radius of cross section \(R / 2\) is \(v_2\). Then \(\frac{v_2}{v_1}=\) ________. 2025 Easy
3. 3. A steel wire with mass per unit length \(7.0 \times 10^{-3}\,kg\,m ^{-1}\) is under tension of \(70\,N\). The speed of transverse waves in the wire will be \(.........m/s\) 2023 Easy
4. 4. The speed of a transverse wave passing through a string of length \(50 \;cm\) and mass \(10\,g\) is \(60\,ms ^{-1}\). The area of cross-section of the wire is \(2.0\,mm ^{2}\) and its Young's modulus is \(1.2 \times 10^{11}\,Nm ^{-2}\). The extension of the wire over its natural length due to its tension will be \(x \times 10^{-5}\; m\). The value of \(x\) is \(...\) 2022 Easy
5. 5. The mass per unit length of a uniform wire is \(0.135\, g / cm\). A transverse wave of the form \(y =-0.21 \sin ( x +30 t )\) is produced in it, where \(x\) is in meter and \(t\) is in second. Then, the expected value of tension in the wire is \(x \times 10^{-2} N\). Value of \(x\) is . (Round-off to the nearest integer) 2021 Easy
6. 6. The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by \(4\, \%\), will be ......... \(\%\) 2021 Medium
7. 7. A transverse wave travels on a taut steel wire with a velocity of \({v}\) when tension in it is \(2.06 \times 10^{4} \;\mathrm{N} .\) When the tension is changed to \(T\). the velocity changed to \(\frac v2\). The value of \(\mathrm{T}\) is close to 2020 Medium
8. 8. A uniform thin rope of length \(12\, m\) and mass \(6\, kg\) hangs vertically from a rigid support and a block of mass \(2\, kg\) is attached to its free end. A transverse short wavetrain of wavelength \(6\, cm\) is produced at the lower end of the rope. What is the wavelength of the wavetrain (in \(cm\) ) when it reaches the top of the rope \(?\) 2020 Medium
9. 9. A wire of density \(9 \times 10^{-3} \,kg\, cm ^{-3}\) is stretched between two clamps \(1\, m\) apart. The resulting strain in the wire is \(4.9 \times 10^{-4}\). The lowest frequency of the transverse vibrations in the wire is......\(HZ\) (Young's modulus of wire \(Y =9 \times 10^{10}\, Nm ^{-2}\) ), (to the nearest integer), 2020 Hard
10. 10. Speed of a transverse wave on a straight wire (mass \(6.0\; \mathrm{g}\), length \(60\; \mathrm{cm}\) and area of cross-section \(1.0\; \mathrm{mm}^{2}\) ) is \(90\; \mathrm{ms}^{-1} .\) If the Young's modulus of wire is \(16 \times 10^{11}\; \mathrm{Nm}^{-2},\) the extension of wire over its natural length is 2020 Easy
11. 11. A heavy ball of mass \(M\) is suspended from the ceiling of car by a light string of mass \(m (m << M)\). When the car is at rest, the speed of transverse waves in the string is \(60\, ms^{-1}\). When the car has acceleration \(a\) , the wave-speed increases to \(60.5\, ms^{-1}\). The value of \(a\) , in terms of gravitational acceleration \(g\) is closest to 2019 Hard
12. 12. Equation of travelling wave on a stretched string of linear density \(5\,g/m\) is \(y = 0.03\,sin\,(450\,t -9x)\) where distance and time are measured in \(SI\) united. The tension in the string is ... \(N\) 2019 Medium
13. 13. A uniform string oflength \(20\ m\) is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is (take \(g= 10 \) \(ms^{-2}\) ) 2016 Easy

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