Wave Motion Equation Speed & Types — Practice Questions

Free NEET Physics multiple-choice questions on Wave Motion Equation Speed & Types. Attempt each question and reveal the answer with a full explanation.

Which of the following functions represents a travelling wave? (kx - t) kx t x 2 - (vt) 2 e -x t The speed of sound in dry air at a certain temperature is v . If the humidity increases, the speed of sound will: Increase Decrease Remain same Become zero The fundamental frequency of a closed organ pipe is 50 Hz . Which of the following frequencies can NOT be produced by this pipe? 100 Hz 150 Hz 250 Hz 350 Hz A wave pulse is described by y = a (x-vt) 2 + b . At t=0 , the pulse is at x=0 . The speed of the wave pulse is: v a b v/a The fundamental frequency of an open organ pipe is 300 Hz . The frequency of the first overtone of this pipe is: 600 Hz 450 Hz 900 Hz 150 Hz The displacement of a wave is represented by y = 0.25 (10 t - 2 x) where x and y are in meters and t is in seconds. The velocity of the wave is: 5 m/s 2 m/s 10 m/s 0.25 m/s The fundamental frequency of a closed organ pipe of length L is f 1 . The fundamental frequency of an open organ pipe of the same length is f 2 . The ratio f 1/f 2 is: 1:2 2:1 1:4 1:1 The tension in a piano wire is 10 N . What should be the tension in the wire to produce a note of double the frequency? 40 N 20 N 80 N 100 N In a longitudinal wave, the distance between a compression and the next rarefaction is: /2 /4 3 /4 A wire of length L and mass M is under tension T . The speed of transverse waves in the wire is: TL/M T/ML TM/L L/TM According to Laplace correction, the speed of sound in a gas is proportional to: 1/ 1/ The fundamental frequency of an open organ pipe is 300 Hz . If one end of the pipe is closed, the new fundamental frequency will be: 150 Hz 600 Hz 300 Hz 450 Hz Which of the following waves cannot be polarized? Sound waves in air Light waves in vacuum Radio waves X-rays For an open organ pipe, the ratio of frequencies of the first three harmonics is: 1:2:3 1:3:5 1:4:9 1:2:4 When sound waves travel from air to water, which of the following remains constant? Frequency Wavelength Velocity Intensity The wavefronts from a point source in an isotropic medium are: Spherical Cylindrical Plane Elliptical A longitudinal wave travels through a metal rod. The time taken by the wave to travel a length L of the rod is (where Y is Young's modulus and is density): L /Y L Y/ 1 L Y/ Y /L A wave is represented by y = 0.1 (100t - 0.2x) where x and y are in meters and t is in seconds. The phase difference between two points separated by a distance of 0.5 m is: 0.1 rad 0.2 rad 0.5 rad rad The speed of sound in an ideal gas at 100 K is v . At what temperature will the speed become 2v ? 400 K 200 K 300 K 800 K When a transverse wave pulse travelling in a denser medium is reflected from the boundary of a rarer medium, the reflected wave has a phase change of: 0 /2 /4 According to the Laplace correction, what is the value of the adiabatic exponent for a diatomic gas like Nitrogen used in calculating the speed of sound? 1.40 1.67 1.33 1.00 A pipe open at both ends has a fundamental frequency f . If one end is closed, the new fundamental frequency will be: f/2 2f f 3f/2 If the phase difference between two points on a wave is 120 , the corresponding path difference is: /3 /6 /2 2 /3 The phase difference between two points separated by a distance x in a wave of wavelength is: 2 x 2 x x 2 x Two pipes, one closed at one end and the other open at both ends, have the same fundamental frequency. The ratio of their lengths L c / L o is: 1/2 2 1/4 1 Which of the following properties of a wave is independent of the others? Amplitude Velocity Wavelength Frequency What is the length of an open organ pipe which resonates with a tuning fork of frequency 480 Hz ? (Speed of sound = 320 m/s and ignore end correction): 0.33 m 0.66 m 0.16 m 0.50 m A wave pulse is described by the equation y(x, t) = 10 2 + (x - 2t) 2 . The speed of the wave pulse is: 2 m/s 4 m/s 0.5 m/s 10 m/s A transverse wave is traveling along a string. The equation is y = 5 [ (0.02x - 4t)] , where x, y are in cm and t in seconds. The maximum particle velocity is: 20 cm/s 4 cm/s 0.02 cm/s 5 cm/s What is the effect of humidity on the velocity of sound? Velocity increases with increase in humidity Velocity decreases with increase in humidity Velocity is independent of humidity Velocity increases with decrease in humidity The frequency of the third harmonic of a closed organ pipe is 450 Hz . The fundamental frequency of this pipe is: 150 Hz 450 Hz 900 Hz 112.5 Hz In a longitudinal wave, the distance between two consecutive regions of maximum pressure is: /2 /4 2 The ratio of the speed of sound in oxygen gas ( M=32 ) to that in hydrogen gas ( M=2 ) at the same temperature is: 1:4 1:16 4:1 16:1 A wave is represented by y = 5 [ (0.01x - 2t)] where x, y are in cm and t in s. The speed of the wave is: 200 cm/s 100 cm/s 50 cm/s 2 cm/s A wave in a string has an amplitude of 2 cm . The wave travels in the +x direction with a speed of 128 m/s and it is noted that 5 complete waves fit in 4 m length of the string. The equation describing the wave is: y = (0.02 m ) (7.85x - 1005t) y = (0.02 m ) (15.7x - 2010t) y = (0.02 m ) (15.7x + 2010t) y = (0.02 m ) (7.85x + 1005t) The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm , the length of the open organ pipe is: 13.3 cm 8 cm 12.5 cm 16 cm If the frequency of a sound wave is doubled and its amplitude is halved, then the intensity of the sound wave will: remain unchanged double quadruple halve A transverse wave is represented by y = A ( t - kx) . For what value of the wavelength is the wave velocity equal to the maximum particle velocity? 2 A A A/2 A A string is cut into three segments of lengths l 1, l 2, l 3 . The fundamental frequencies of these segments are n 1, n 2, n 3 respectively. The fundamental frequency n of the original string is given by: 1/n = 1/n 1 + 1/n 2 + 1/n 3 n = n 1 + n 2 + n 3 n = n 1 + n 2 + n 3 n 2 = n 1 2 + n 2 2 + n 3 2 A wave of frequency 500 Hz has a velocity of 350 m/s . The distance between two nearest points which are 60 out of phase is: 70/6 cm 70 cm 11.6 cm 6 cm The velocity of sound in a gas is v and the root mean square velocity of the gas molecules is c rms . The ratio v/c rms is: /3 3/ /3 3/ If the density of a gas at constant temperature is doubled, the speed of sound in the gas will: Remain the same Be doubled Be halved Become four times A closed organ pipe has a fundamental frequency of 50 Hz . The frequency of the second overtone is: 250 Hz 150 Hz 100 Hz 200 Hz The temperature at which the speed of sound in air becomes double of its value at 0 C is: 819 C 273 C 546 C 1092 C A string of length 2 m is fixed at both ends and vibrates in 3 loops. The wavelength of the standing wave is: 1.33 m 2 m 0.67 m 3 m If the equation of a transverse wave is y = 2 (2 x - 10 t) , what is the ratio of maximum particle velocity to wave velocity? 4 2 10 1 The power transmitted by a sinusoidal wave on a string is proportional to: Square of the amplitude and square of the frequency Square of the amplitude and the frequency Amplitude and square of the frequency Square root of amplitude and frequency In a resonance tube experiment, the first resonance is obtained at 16 cm and the second resonance at 49 cm . The end correction for the tube is: 0.5 cm 1.0 cm 1.5 cm 2.0 cm A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column now is: f f/2 2f 3f/4 The wave function of a pulse is y = 5 (x - 4t) 2 + 2 . The velocity of the pulse is: 4 m/s in +x direction 4 m/s in -x direction 2 m/s in +x direction 5 m/s in +x direction A heavy rope of length L and mass M hangs vertically from a rigid support. The speed of a transverse wave pulse at a distance x from the lower end is: gx gL 2gx g(L-x) If a tuning fork is used to excite a resonance tube, and the temperature of the air in the tube increases, the resonance length will: Increase Decrease Remain the same Become zero A wave pulse is described by y = a b + (x - ct) 2 . What is the velocity of the pulse? c b a/c c/b A sonometer wire of length L is vibrating in its fundamental mode. If the tension is increased by 21 % , the percentage change in the fundamental frequency is: 10 % 21 % 44 % 5 % A mixture of 2 moles of Helium (monatomic) and 2 moles of Hydrogen (diatomic) is used. The speed of sound in this mixture at temperature T is proportional to: mix T / M mix T / M mix mix T mix T A wave pulse is reflected from a rigid boundary. The reflected pulse has a phase change of: radians 0 radians /2 radians 2 radians The average energy density (energy per unit volume) of a plane progressive wave of amplitude A , frequency f in a medium of density is: 2 2 f 2 A 2 2 f 2 A 2 4 2 f 2 A 2 1 2 2 f 2 A 2 When the temperature of the air in which a tuning fork is vibrating increases, the frequency of the tuning fork: Decreases slightly Increases slightly Remains the same First increases then decreases An open organ pipe is filled with a gas of density 1 . Another identical pipe is filled with a gas of density 2 . If the pressures are the same and both gases are diatomic, the ratio of their fundamental frequencies is: 2 / 1 1 / 2 2 / 1 1 / 2 If the length of a closed organ pipe is 1.5 m and the velocity of sound is 330 m/s , the frequency of the second overtone is: 275 Hz 110 Hz 165 Hz 550 Hz A transverse wave is described by y = A [2 (ft - x/ )] . The maximum particle velocity is equal to 4 times the wave velocity if: = A / 2 = A = 2 A = 4 A In a sonometer wire, the tension is made 4 times and the length is doubled. The fundamental frequency will: Remain same Become doubled Become half Become four times The speed of sound in Hydrogen gas is 1284 m/s at 0 C . The speed of sound in Oxygen gas at 0 C is: 321 m/s 642 m/s 428 m/s 160 m/s Two strings of the same material and same length have radii r and 2r . If they are stretched by the same tension, the ratio of their fundamental frequencies is: 2:1 1:2 4:1 1:4 The velocity of sound in a gas at pressure P and density is v . If the pressure is increased to 4P while keeping the temperature constant, the new velocity will be: v 2v 4v v/2 A plane wave is represented by x = 1.2 (314t + 12.56y) where x and y are in meters and t in seconds. The direction of propagation is: Negative y-direction Positive y-direction Negative x-direction Positive x-direction A wave pulse traveling on a string is reflected from a free end (boundary of a rarer medium). The phase change produced upon reflection is: 0 /2 2 If the length of an open organ pipe is 50 cm , the frequency of the second overtone is (speed of sound = 340 m/s ): 1020 Hz 340 Hz 680 Hz 510 Hz A resonance tube is used to determine the speed of sound. If the first resonance length is 20 cm and the second resonance length is 62 cm , the end correction is: 1 cm 2 cm 0.5 cm 4 cm If the tension in a sonometer wire is increased by 44 % , the percentage increase in its fundamental frequency is (assume length is constant): 20 % 44 % 22 % 10 % Two strings of the same material have radii in ratio 1:2 and tensions in ratio 1:1 . If their lengths are equal, the ratio of their fundamental frequencies is: 2:1 1:2 1:4 4:1 What is the ratio of the frequency of the first overtone of an open pipe to the first overtone of a closed pipe of the same length? 4/3 2/3 1/2 3/4 If the pressure of a gas is doubled at constant temperature, the speed of sound in the gas: Remains the same Is doubled Is quadrupled Is halved In a resonance tube experiment, the first resonance is at 15 cm and the second resonance is at 47 cm . The wavelength of sound used is: 64 cm 32 cm 47 cm 30 cm The ratio of the speed of sound in a monatomic gas to the root mean square speed of its molecules at the same temperature is: 5/9 3/5 5/3 2/3 A sonometer wire of length L vibrates in fundamental mode with frequency n . If the tension is increased by 69 % , the new frequency will be: 1.3n 1.69n 0.3n 1.44n If a string fixed at both ends is divided into three segments of lengths l 1, l 2, l 3 such that their fundamental frequencies are n 1, n 2, n 3 , then the fundamental frequency n of the original string is: 1/n = 1/n 1 + 1/n 2 + 1/n 3 n = n 1 + n 2 + n 3 n 2 = n 1 2 + n 2 2 + n 3 2 n = n 1 n 2 n 3 A string of length L is fixed at both ends. If it vibrates in its fourth harmonic, the number of nodes and antinodes formed are respectively: 5 and 4 4 and 5 4 and 3 3 and 4 A tuning fork with frequency 800 Hz produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Successive resonances are observed at lengths 9.75 cm and 31.25 cm . The speed of sound in air is: 344 m/s 172 m/s 516 m/s 312 m/s The ratio of the speed of sound in nitrogen gas to that in helium gas at the same temperature is: 2/7 1/7 3/5 6/5 In a sound wave, the phase difference between the displacement wave and the pressure wave is: /2 2 Zero Two open organ pipes of lengths 50 cm and 50.5 cm produce 3 beats per second when sounded together. The velocity of sound in air is: 303 m/s 330 m/s 340 m/s 297 m/s The speed of transverse waves in a solid rod of density and Young's modulus Y is proportional to: Y/ / B/ Y The speed of sound in a mixture of n 1 moles of helium and n 2 moles of oxygen at temperature T depends on the effective molar mass M eff and effective adiabatic exponent mix . If n 1 = n 2 , the value of mix is: 1.5 1.63 1.4 1.67 The ratio of the speed of sound in Hydrogen gas to that in Helium gas at the same temperature is: 42/5 5/3 2/1 7/5 The pressure amplitude P 0 in a sound wave is related to the displacement amplitude A by the formula (where B is bulk modulus and k is wave number): P 0 = BkA P 0 = B/kA P 0 = Ak/B P 0 = B A 2 In a dispersive medium, the wave velocity v depends on wavelength as v = a/ . The group velocity v g is related to v as: v g = 2v v g = v/2 v g = v v g = 0 The ratio of the speed of longitudinal waves to the speed of transverse waves in a long solid wire of Young's modulus Y , Poisson's ratio = 0.5 , and density is (Assume G = Y/[2(1+ )] , where G is Shear Modulus): 3 2 1 3 A transverse wave is described by y = 0.5 (2x - 4t) , where x and y are in meters and t is in seconds. The velocity of the wave is: 2 m/s 4 m/s 0.5 m/s 8 m/s A wave is described by y = A (kx - t) . The particle velocity is leading the wave velocity in phase by /2 when the particle is at: Mean position Extreme position Midway between mean and extreme Nowhere The speed of sound in oxygen ( M = 32 ) at a certain temperature is V . The speed of sound in helium ( M = 4 ) at the same temperature is: 32 3 V 2 2 V 3V 4V A mixture of 2 moles of Helium (monatomic, = 5/3 ) and 1 mole of Hydrogen (diatomic, = 7/5 ) is prepared. The effective value of adiabatic exponent mix for the mixture is approximately: 1.57 1.53 1.48 1.60