**JEE Main Previous Year Papers Questions With Solutions Physics Waves**

**Multiple Choice with ONE correct answer**

**1.A wave represented by the equation y = acos(kx â€” wt) is superposed with another wave to form a stationary wave such that point x=0 is a node. The equation for the other wave is [1988-1 mark]**

**2. An object of specific gravity p is hung from a thin steel wire. The fundamental frequency for trans verse standing waves in the wire is 300 Hz. The object is immersed in water so that one half of its volume is submerged. The new fundamental fre quency in Hz is [1995-2 marks]**

**3.The extension in a string, obeying Hooke’s law, is x . The speed of sound in the stretched string is v. If the extension in the string is increased to 1.5 x , the speed of sound will be [1996-2 marks]**

** a) 1.22 v b) 0.61 v c) 1.50 v d) 0.75 v**

**4.An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe . The fundamental frequency of the open pipe is :[1996-2 marks]**

** a) 200 Hz b) 300 Hz**

** c) 240 Hz d) 480 Hz**

**5.A whistle giving out 450 Hz approaches a station ary observer at a speed of 33 m/s. The frequency heard by the observer in Hz is : (speed of sound = 330 m/s) [1997-1 mark]**

** a) 409 b) 429 c) 517 d) 500**

**6.A travelling wave in a stretched string is described by the equation y = A sin (kx – wt) . The maximum particle velocity is : [1997-1 mark]**

** a) Aw b) w/k c) dw/dk d) x/t**

**7.A train moves towards a stationary observer with speed 34m/s. The train sounds a whistle and its frequency registered by the observer is f1. If the train’s speed is reduced to 17m/s, the frequency registered is f _{2}. If the speed of sound is 340m/s then the ratio f1/f_{2} is[2000-2 marks]**

**a) 18/19 b) 1/2 c) 2 d) 19/18**

**8.Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension . Both the strings vibrate in their fundamental nodes, the one of length L with frequency f1 and the other with frequency f _{2}. The ratio f1/f_{2} is given by [2000-2 marks]**

**a) 2 b) 4 c) 8 d) 1**

**9.Two pulses in a stretched string whose centres are initially 8 cm apart are moving towards each other as shown in the figure. The speed of each pulse is 2 cm/s. After 2 seconds, the total energy of the pulses will be [2001-2 marks]**

** a) zero**

** b)purely kinetic**

** c)purely potential**

** d)partly kinetic and partly potential**

**10.The ends of a stretched wire of length L are fixed at x = 0 and x = L. In one experiment, the displacement of the wire is y _{t} = A sin(px/L) sin wt and energy is Ej and in another experiment its displacement is y_{2}=Asin(2px/L) sin 2wt and energy is E_{2}. Then [2001-1 marks]**

**a) E**

_{2}= E1 b) E_{2}= 2E1**c) E**

_{2}= 4E1 d) E_{2}= 16E1**11.A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train A records a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that of train A is [2002-2 marks]**

** a) 242/252 b) 2 c)5/6 d) 11/6**

**12.A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9 kg is suspended from the wire. When this mass is re placed by a mass M, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of M is [2002-2 marks]**

** a) 25 kg b) 5 kg c) 12.5 kg d) 1/25 kg**

**13.A police car moving at 22 m/s, chases a motorcyclist. The police man sounds his horn at 176Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of the motorcycle, if it is given that he does not observe any beat. [2003-2 marks]**

** a) 33 m/s b) 22 m/s c) zero d) 11 m/s**

**14.In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1m. When this length is changed to 0.35m, the same tuning fork resonates with the first overtone. Calculate the end correction. [2003-2 marks]**

** a) 0.012 m b) 0.025 m**

** c) 0.05 m d) 0.024m**

**15.A pipe of length l1 closed at one end is kept in a chamber of gas of density p1 . A second pipe open at both ends is placed in a second chamber of gas of density p _{2}. The compressibility of both the gases is equal. Calculate the length of the second pipe if frequency of first overtone in both the cases is equal [2004-2 marks]**

**16.A source of sound of frequency 600 Hz is placed inside water. The’speed of sound in water is 1500m/s and in air it is 300m/s. The frequency of sound recorded by an observer who is standing in air, is [2004-2 marks]**

** a) 200 Hz b) 3000 Hz c) 120 Hz d) 600 Hz**

**17.In a resonance tube with tuning fork of frequency 512 Hz, first resonance occurs at water level equal to 30.3cm and second resonance occurs at 63.7 cm. The maximum possible error in the speed of sound is [2005-2 marks]**

** a) 51.2cm/s b) 102.4cm/s**

** c) 204.8cm/ s d) 153.6cm/s**

**18.An open pipe is in resonance in 2 ^{nd} harmonic with frequency f1. Now one end of the tube is closed and frequency is increased to f_{2} such that the reso nance again occurs in _{n}th harmonic. Choose the correct option [2005-2 marks]**

**19.A massless rod is suspended by two identical strings AB and CD of equal length. A block of mass m is suspended from point O such that BO is equal to â€˜x’. Further, it is observed that the frequency of 1 ^{st} harmonic (fundamental frequency) in AB is equal to 2^{nd} harmonic frequency in CD. Then, [2006-3 marks]**

**20.In the experiment to determine the speed of sound , using a resonance column, [2007-3 marks]**

** a)prongs of the tuning fork are kept in a vertical plane**

** b)prongs of the tuning fork are kept in a horizontal plane**

** c)in one of the two resonaces observed, the length of the resonating air column is close to the wavelength of sound in air.**

** d)in one of the two resonances observed, the length of the resonating air column is close to half of the wavelength of sound in air.**

**21.A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time t, the snap shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is.[2008]**

**22.A vibrating string of certain length / under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n.Now when the tension of the string is slightly increased the number of beats reduces to 2 per second. Assuming the velocity of sound in air to be 340m/s, the frequency n of the tuning fork in Hz is [2008]**

** a) 344 b) 336 c) 117.3 d) 109.3**

**23.A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it reso nates with the fundamental frequency of the pipe. If the tension in the wire is 50 N and the speed of sound is 320 ms ^{1}, the mass of the string is**

**a) 5 grams b) 10 grams c) 20 grams d) 40 grams**

**24.A police car with a siren of frequency 8kHz is moving with uniform velocity 36km/hr towards a tall building which reflects the sound waves. The speed of sound in air is 320 m/s. The frequency of the siren heard by the car driver is (2011)**

** a) 8.50 kHz b) 8.25 kHz**

** c) 7.75 kHz d) 7.50 kHz**

**Multiple Choice with ONE or More Than ONE correct answers**

** 25.A wave equation which gives the displacement along the y-direction is given by y = 10 ^{-4} sin (60t + 2x) where x and y are in metre and t is time in second. This represents a wave**

**27.An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the col umn in cm is (V=330ms ^{_1}) [1985-2 marks]**

**a) 31.25 b) 62.50**

**c) 93.75 d) 125**

**28.A tube closed at one end and containing air produces, when excited, the fundamental note of frequency 512 Hz. If the tube is open at both ends the fundamental frequency that can be excited is (in Hz) [1986-2 marks]**

** a) 1024 b) 512 c)256 d) 128**

**29.The displacement of particles in a string stretched in the x-direction is represented by y. Among the following expressions for y, those describing wave motion are [1987-2 marks]**

**30.An organ pipe P1 closed at one end vibrating in its first harmonic and another pipe P _{2} open at ends vibratting in its third harmonic are in resonance with a given tuning fork. The ratio of the length of P1 to that of P_{2} is [1988-2 marks]**

**a) 8/3 b)3/8 c)l/6 d) 1/3**

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