Wave Motion & Waves on String PYQs Set 5 (PDF)

Set 5 of 5 · Questions 121-141 of 141

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Mere Teacher · Previous Year Questions JEE Main Physics · Wave Motion & Waves on String · Set 5 (Q121-141)
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121. $A stretched string fixed at both ends has m nodes, then the length of the string will be$ (1) $(m - 1) \frac{λ}{2}$ (2) $\frac{( m + 1 ) λ}{2}$ (3) $\frac{mλ}{2}$ (4) $(m - 2) \frac{λ}{2}$ 122. $In a sonometer experiment, the string of length L under tension vibrates in second overtone between two bridges. The amplitude of vibration is maximum at$ (1) $\frac{L}{3}, \frac{2 L}{3}, \frac{5 L}{6}$ (2) $\frac{L}{8}, \frac{L}{4}, \frac{L}{2}$ (3) $\frac{L}{2}, \frac{L}{4}, \frac{L}{6}$ (4) $\frac{L}{6}, \frac{L}{2}, \frac{5 L}{6}$ 123. $If n_{1}, n_{2} and n_{3} are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by:$ (1) $\frac{1}{n} = \frac{1}{n _{1}} + \frac{1}{n _{2}} + \frac{1}{n _{3}}$ (2) $\frac{1}{n} = \frac{1}{n _{1}} + \frac{1}{n _{2}} + \frac{1}{n _{3}}$ (3) $n = n_{1} + n_{2} + n_{3}$ (4) $n = n_{1} + n_{2} + n_{3}$ 124. $A glass tube is open at both the ends. A tuning fork of frequency f resonates with the air column inside the tube. Now the tube is placed vertically inside water so that half the length of the tube is filled with water. Now the air column inside the tube is in unison with another fork of frequency f^{’} . Then$ (1) $f^{’} = f$ (2) $f^{’} = 4 f$ (3) $f^{’} = 2 f$ (4) $f^{’} = f /2$ 125. $The length of the wire between two ends of a sonometer is 100 cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio 1:3: 5.$ (1) $\frac{1500}{23} cm, \frac{500}{23} cm$ (2) $\frac{1500}{23} cm, \frac{300}{23} cm$ (3) $\frac{300}{23} cm, \frac{1500}{23} cm$ (4) $\frac{1500}{23} cm, \frac{2000}{23} cm$ 126. $The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, y_{1} (x, t) = 4 sin (kx - ωt) and y_{2} (x, t) = 2 sin (kx - ωt + \frac{2 π}{3}), are: (Take the angular frequency of initial waves same as ω)$ (1) $(3, \frac{π}{6})$ (2) $(23, \frac{π}{6})$ (3) $(6, \frac{2 π}{3})$ (4) $(6, \frac{π}{3})$ 127. $Three harmonic waves having equal frequency v and same intensity I_{o}, have phase angles 0, \frac{π}{4} and -, \frac{π}{4} respectively. When they are superimposed the intensity of the resultant wave is close to:$ (1) $I_{o}$ (2) $0$ (3) $5.8 I_{0}$ (4) $0.2 I_{0}$ 128. $The equation of simple harmonic progressive wave is given by y = asin 2 π (bt - cx) . The maximum particle velocity will be half the wave velocity if c =$ (1) $2 πa$ (2) $\frac{1}{4 π a}$ (3) $\frac{1}{2 π a}$ (4) $4 πa$ 129. $The equation of a simple harmonic wave is given by y = 3 sin \frac{π}{2} (50 t - x), where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is$ (1) $2 π$ (2) $\frac{3}{2} π$ (3) $3 π$ (4) $\frac{2}{3} π$ 130. $A steel wire with mass per unit length 7.0 \times 1 0^{- 3} kg m^{- 1} is under tension of 70 N. The speed of transverse waves in the wire will be:$ (1) $200 π m/s$ (2) $100 m/s$ (3) $10 m/s$ (4) $50 m/s$ 131. $The wave described by y = 0.25 sin (10 π x - 2 π t), where x and y are in meters and t in seconds, is a wave travelling along the$ (1) $+ vex direction with frequency 1 Hz and wavelength λ = 0.2 m .$ (2) $-ve x direction with amplitude 0.25 m and wavelength λ = 0.2 m .$ (3) $-ve x direction with frequency 1 Hz.$ (4) $+ vex direction with frequency π Hz and wavelength λ = 0.2 m .$ 132. $Two strings (A, B) having linear densities μ_{A} = 2 \times 10^{- 4} kg / m and, μ_{B} = 4 \times 10^{- 4} kg / m and lengths L_{A} = 2.5 m and L_{B} = 1.5 m respectively are joined. Free ends of A and B are tied to two rigid supports C and D, respectively creating a tension of 500 N in the wire. Two identical pulses, sent from C and D ends, take time t_{1} and t_{2}, respectively, to reach the joint. The ratio t_{1} / t_{2} is :$ (1) $1.90$ (2) $1.67$ (3) $1.08$ (4) $1.18$ 133. $A wire PQ has length 4.8 m and mass 0.06 kg . Another wire QR has length 2.56 m and mass 0.2 kg . Both wires have same radii and are joined as a single wire. This wire is under tension of 80 N . A wave pulse of amplitude 3.5 cm is sent along the wire PQ from end P . The time taken by the wave to reach the other end of single wire is(No power is dissipated during propagation)$ (1) $0.1 s$ (2) $0.12 s$ (3) $0.14 s$ (4) $0.16 s$ 134. $With the propagation of a longitudinal wave through a material medium, the quantities transmitted in the propagation direction are$ (1) $energy, momentum and mass$ (2) $energy$ (3) $energy and mass$ (4) $energy and linear momentum$ 135. $A progressive wave travelling along the positive x -direction is represented by y (x, t) = Asin (kx - ωt + φ) . Its snapshot at t = 0 is given in the figure. For this wave, the phase φ is:$ (1) $- \frac{π}{2}$ (2) $π$ (3) $0$ (4) $\frac{π}{2}$ 136. $Doppler shift in frequency does not depend upon$ (1) $The frequency of the wave produced$ (2) $The velocity of the source$ (3) $The velocity of the observer$ (4) $Distance from the source to the listener$ 137. $Match List I with List II List I A. Troposphere B. E-Part of Stratosphere C. F_{2} -Part of Thermosphere D. D-Part of Stratosphere List II I. Approximate 65-75 km over Earth’s surface II. Approximate 300 km over Earth’s surface III. Approximate 10 km over Earth’s surface IV. Approximate 100 km over Earth’s surface Choose the correct answer from the options given below:$ (1) $A-III, B-IV, C-Il, D-I$ (2) $A-I, B-II, C-IV, D-III$ (3) $A-I, B-IV, C-III, D-II$ (4) $A-III, B-II, C-I, D-IV$ 138. $Stationary waves can be produced in$ (1) $only solid and gaseous media$ (2) $only liquid and gaseous media$ (3) $only solid and liquid media$ (4) $solid, liquid and gaseous media.$ 139. $Four harmonic waves of equal frequencies and equal intensities I_{0} have phase angles 0, \frac{π}{3}, \frac{2 π}{3} and π. When they are superposed, the intensity of the resulting wave is n I_{0} . The value of n is:$ 140. $The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is 60 m s^{- 1} . The area of cross-section of the wire is 2.0 mm^{2} and its Young's modulus is 1.2 \times 1 0^{11} N m^{- 2} . The extension of the wire over its natural length due to its tension will be x \times 1 0^{- 5} m. The value of x is_______.$ 141. $Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by y = (10 cos π x sin \frac{2 πt}{T}) cm The amplitude of the particle at x = \frac{4}{3} cm will be _______cm.$