Waves and sound-04-OBJECTIVE ASSIGNMENTS

OBJECTIVE ASSIGNMENTS 1. The amplitude of velocity of a particle is given by the condition for single resonant frequency is (a) (b) (c) (d) . 2. Which of the following statements is correct (a) Both sound and light waves in air are longitudinal (b) Both sound and light waves in air are transverse (c) Sound waves in air are transverse while light longitudinal (d) Sound waves in air are longitudinal while light transverse 3. Two sound waves are respectively and The phase difference between the two waves is (a) (b) (c) (d) . 4. If the equation of a progressive wave is given by then which of the following is correct (a) (b) (c) (d) . 5. Velocity of sound is measure in hydrogen and oxygen gases at a given temperature. The ratio of the two velocities will be (a) 1 : 4 (b) 4 : 1 (c) 1 : 1 (d) 32 : 1. 6. If at a place the speed of a sound wave of frequency 300 Hz is V, the speed of another wave of frequency 150 Hz at the same place will be (a) V (b) V/2 (c) 2V (d) 4V. 7. The intensity of a sound wave gets reduced by 20% on passing through a slab. The reduction in intensity on passage through two such consecutive slabs is (a) 40% (b) 36% (c) 30% (d) 50%. 8. The amplitude of sound is doubled and the frequency is reduced to one-fourth. The intensity of sound at the same point will be (a) Increased by a factor of 2 (b) Increased by a factor of 4 (c) Decreased by a factor of 2 (d) Decreased by a factor 4. 9. A wave travels uniformly in all directions from a point source in an isotropic medium. The displacement of the medium at any point distance from the source may be represented by ( is a constant representing strength of source) (a) (b) (c) (d) . 10. A man standing between two cliffs hears the first echo of a sound after 2 sec and the second echo 3 sec after the initial sound. If the speed of sound be 330 m/s, the distance between the two cliffs should be (a) 1650 m (b) 990 m (c) 825 m (d) 660 m. 11. An open pipe is suddenly closed with the result that the second overtone of the closed pipe is found to be higher in frequency by 100 Hz than the first overtone of the original pipe. The fundamental frequency of open pipe will be (a) 100 Hz (b) 300 Hz (c) 150 Hz (d) 200 Hz. 12. Organ pipe closed at one end vibrating in its first harmonic and another pipe open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of to that of is (a) 8/3 (b) 1/6 (c) 1/2 (d) 1/3. 13. A train moves towards a stationary observer with speed 34 m/s. The train sound a whistle and its frequency registered by the observer is . If the train’s speed is reduced to 17 m/s, the frequency registered is . If the speed of sound is 340 m/s then the ratio is (a) (b) (c) 2 (d) . 14. The extension in a string, obeying Hookes’ law, is x. The speed of the wave in the stretched string is . If the extension in the string is increased to 1.5 x, the speed of the wave in the string will be (a) 1.22 v (b) 0.61 v (c) 1.50 v (d) 0.75 v. 15. Figure shows the shape of part of a long string in which transverse waves are produced by attaching one end of the string to tuning fork of frequency 250 Hz. What is the velocity of the waves ? (a) (b) (c) (d) . 1. The amplitude of velocity of a particle acted on by a force, F cos , along the x-direction is given by where are constants and . For what value of does the resonance occur (a) (b) (c) (d) . 2. Three progressive waves A, B and C are shown in figure. With respect to wave A (a) The wave C lags behind in phase by and B leads by (b) The wave C leads in phase by and B lags behind by (c) The wave C leads in phase by and B lags behind by (d) The wave C lags behind in phase by and B leads by . 3. The displacement y (in cm) produced by a simple harmonic wave is given by The period and maximum velocity of the particle in the medium respectively will be given by (a) (b) (c) (d) . 4. The equation of a wave is given by . If the displacement is 5 cm at , then the total phase at s will be (a) (b) (c) (d) . 5. The intensity of a plane progressive wave of frequency 1 kHz is . If the density of air is 1.3 kg/m3 and the speed of sound is equal to 330 m/s, then pressure amplitude of the wave is (a) (b) (c) (d) . 6. Out of the given waves (A), (B), (C) and (D), emitted by four different sources respectively; perfect interference phenomena will be observed in space under appropriate conditions when (a) (b) (c) (d) . 7. Two tuning forks A and B are sounded together and 8 beats per second are heard. A is in resonance with a 32 cm air column closed at one end and B is in resonance when length of air column is increase by 1 cm. The frequencies of forks A and B are (a) 264 Hz, 256 Hz (b) 272 Hz, 264 Hz (c) 528 Hz, 520 Hz (d) 520 Hz, 512 Hz. 8. A source of frequency f gives 5 beat/s when sounded with source of frequency 200 Hz. The second harmonic of source gives 10 beat/s when sounded with a source of frequency 420 Hz. The value of f is (a) 200 Hz (b) 210 Hz (c) 205 Hz (d) 195 Hz. 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 (a) zero (b) purely kinetic (c) purely potential (d) partly kinetic and partly potential. 10. A machine gun is mounted on a tank moving at a speed of 20 towards a target with the gun pointing in the direction of motion of the tank. The muzzle speed of the bullet equals the speed of sound = 340 . If, at the time of firing, the target is 500 m away from the tank, then (a) The sound arrives at the target later than the bullet (b) The sound arrives at the target earlier than the bullet (c) Both sound and bullet arrive at the target at the same time (d) The bullet will never arrive at the target. 11. In a sonometer wire, the tension is maintained suspending a 50.7 kg mass from the free end of the wire. The suspended mass has a volume of 0.0075 m3. The fundamental frequency of the wire is 260 Hz. If the suspended mass is completely submerged in water, the fundamental frequency will become (a) 240 Hz (b) 220 Hz (c) 230 Hz (d) 280 Hz. 12. A source S emits electromagnetic waves which are detected by the detector D kept at a distance of from the source. The waves directly received from S and reflected by a layer d above the ground are found to be in phase. If the layer moves up by a distance h = 0.01d, the interfering waves are once again in phase. The wavelength of the waves from the source is about (a) 0.04d (b) 0.08d (c) 0.02d (d) 0.01d. 13. In a standing wave pattern obtained in a tube filled with iodine, due to vibrations of frequency 800 cycle/sec, the distance between eleven consecutive nodes is found to be 1 m, when the temperature of iodine vapours is 352ºC. If the temperature is 127ºC, the distance between consecutive nodes is (a) 0.08 m (b) 0.072 m (c) 1.25 m (d) m. 14. A railway engine whistling at a constant frequency moves with a constant speed. It goes part a stationary observer beside the railway track. Which of the following graphs best represents the variation of frequency of the sound (n) heard by the observer with time (t) (a) (b) (c) (d) . 15. Two observers A and B start from the point O to move due E and due W respectively at time t = 0, with the same constant speed u m/s, when a source, situated d metre due S of their starting point O emits a continuous note of frequency n hertz. The velocity of sound is v m/s and there is no wind. In respect of the sound received by the two observers, which of the following statements will be true ? (a) The apparent frequencies of the note as heard by the two observers will be the same and given by (b) The apparent frequency of the note as heard by A will be greater than that heard by B (c) The apparent frequency of the note as heard by A will be smaller than that heard by B (d) The frequencies of the note as heard by the observers A and B will be the same as the real frequency n hertz. SUBJECTIVE ASSIGNMENT 1. A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air at 20º C ( )? 2. A wave traveling along a string is described by, , in which the numerical constants are in SI units ( ). Calculate (a) The amplitude, (b) The wavelength, and (c) The period and frequency of the wave. Also calculate the displacement of the wave at a distance cm and time ? 3. A pipe 30 cm long is open at both ends. Which harmonic mode of the pipe is resonantly excited by a 1.1 kHz source? Given velocity of sound = 330 m . 4. A steel rod 100 cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be 2.53 kHz. What is the speed of sound in steel? 5. A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 425 Hz source ? Will this same source be in resonance with the pipe if both ends are open? (speed of sound ). 6. A metre-long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a tuning fork of frequency 340 Hz) when the tube length is 25.5 cm or 79.3 cm. Estimate the speed of sound in air at the temperature of the experiment. Ignore edge effect. 7. Two sitar strings A and B playing the note ‘Dha’ are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B is slightly increased and the beat frequency is found to reduce to 3 Hz. What is the original frequency of B is the frequency of A is 427 Hz? 8. The sirens of two fire engines have a frequency of 650 Hz each. A man hears the sirens from the two engines, one approaching him with a speed of 36 km and the other receding from him at a speed of 54 km . What is the difference in frequency of the two sirens heard by the man? Take the speed of sound to be 340 . 9. A train standing at the outer signal of a railway station blows a whistle of frequency 400 Hz instill air. (i) what is the frequency of the whistle for a platform observer when the train (a) Approaches the platform with a speed of 10 ? (b) Recedes from the platform with a speed of 10 ? (ii) What is the speed of sound in each case? Given speed of sound in still air = 340 . 10. A transverse harmonic wave on a string is described by where are in cm and in s. The positive direction is from left to right. (i) Is this a traveling or a stationary wave ? If it is traveling, what are the speed and direction of its propagation? (ii) What are its amplitude and frequency? (iii) What is the initial phase at the origin? (iv) What is the least distance between two successive crests in the wave? 11. For the traveling harmonic wave where and are in cm and in s. What is the phase difference between oscillatory motions at two points separated by a distance of (i) 4 m, (ii) 0.5 m (iii) (iv) ? 12. Two harmonic waves have the same displacement amplitude of cm and their angular frequencies are 500 and 5000 . Calculate (i) particle velocity amplitude, and (ii) particle acceleration amplitude. 13. Transverse wave of amplitude 0.1 m is generated at one end (x = 0) of a long string by a tuning fork of frequency 500 Hz. At a certain instant of time, the displacement of particle at m is -0.05 m and of particle at m is + 0.05 m. How long does the wave take to travel from and ? 14. A pipe of length 20 cm is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 245 Hz sourcs? The speed of sound = 340 . 15. A train standing at a certain distance from a railway platform is blowing a whistle of frequency 500 Hz. If the speed of sound is 340 , the frequency and wavelength of the sound of the whistle heard by a man running towards the engine with a speed of 10 respectively. 1. Two tuning forks A and B produce 10 beats per second when sounded together. On loading the fork A slightly it was observed that 15 beats are heard in one second. If the frequency of the fork B is 480 Hz, calculate the frequency of the fork A before loading. 2. The length of the wire shown in figure between the pulleys is 1.5 m and its mass is 12.0 g. Find the frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulleys at rest. 3. A sonometer wire of length 110 cm is stretched with a tension T and fixed at its ends. The wire is divided into three segments by placing two bridges below it. Where should the bridges be placed so that the fundament frequencies of the segments are in the ratio 1 2 3 ? 4. Figure shows an aluminium wire of length 60 cm joined to a steel wire of length 80 cm and stretched between two fixed supports. The tension produced is 40 N. The cross-sectional area of the steel wire is 1.0 mm2 and that the aluminum wire is 3.0 mm2. What could be the minimum frequency of a tuning fork which can produce standing waves in the system with the joint as a node? The density of aluminium is 2.6 g/cm3 and that of steel is 7.8 g/cm3. 5. AB is a cylinder of length 1.0 m, fitted with a thin flexible diaphragm C at the middle and two thin flexible diaphragms A and B at the ends (see figure). The portions AC and BC contain hydrogen and oxygen respectively. The diaphragms A and B are set into vibrations of the same frequency. What is the minimum frequency of these vibrations for which the diaphragm C is a node ? Under the conditions of the experiment, the velocity of sound in hydrogen is 1100 and in oxygen is 300 . 6. A train running at 108 km/h towards east whistles at a dominant frequency of 500 Hz. Speed of sound in air is 340 m/s. (a) What frequency will a passenger sitting near the open window hear? (b) What frequency will a person standing near the train has just passed? (c) A wind starts blowing towards east at a speed of 36 km/h. Calculate the frequencies heard by the passenger in the train and by the person standing near the track. 7. Calculate the number of beats heard per second if three sources of sound of frequencies 400 Hz, 401 Hz and 402 Hz producing sounds of equal amplitude are sounded together. 8. A source is moving along a circle with constant speed m/s in clockwise direction while an observer is stationary at point with respect to the centre of circle. Frequency emitted by the source is . (a) Find the coordinates of source when observer records the maximum and minimum freq. (b) Find the value of maximum and minimum frequency. Take speed of sound m/s 9. A wire of uniform cross-section is stretched between two points 1 m apart. The wire is fixed at one end and a weight of 9 kg is hung over a pulley at the other end produces fundamental frequency of 750 Hz. (a) What is the velocity of transverse waves propagating in the wire? (b) If now the suspended weight is submerged in a liquid of density (5/9) that of the weight, what will be the velocity and frequency of the waves propagating along the wire? 10. A long horizontal pipe is fitted with a piston of mass 10 kg which is connected to another mass 10.5 kg by a string passing over a frictionless pulley. A source of sound of frequency 512 Hz is placed in front of the piston. Initially the position is almost is touch with the source and it moves away from the source when the hanging mass is released. Find the times at which maximum sound will be heard. Assume the string is horizontal between pulley and piston. There is no friction and velocity of sound in air is 340 m/s. 1. The equation for the vibration of a string, fixed at both ends vibrating in its third harmonic, is given by . (a) What is the frequency of vibration? (b) What are the positions of the nodes? (c) What is the length of the string? (d) What is the wavelength and the speed of two traveling waves that can interfere to give this vibration? 2. A metal wire of diameter 1 mm is held on two knife edges separated by a distance 50 cm. The tension in the wire is 100 N. The wire vibrating with its fundamental frequency and a vibrating tuning fork together produce 5 beats per second. The tension in the wire is then reduced to 81 N. When the two are excited beats and heard again at the same rate. Calculate (a) the frequency of the fork and (b) the density of the material of the wire. 3. A string 25 cm long and having a mass of 2.5 g is under tension. A pipe closed at one end is 40 cm long. When the string is set vibrating in its first overtone and the air in the pipe in its fundamental frequency, 8 beats per second are heard. It is observed that decreasing the tension in the string decreases the beat frequency. If the speed of sound in air is 320 , find the tension in the string. 4. A tube of a certain diameter and of length 48 cm is open at both ends. Its fundamental frequency of resonance is found to be 320 Hz. The velocity of sound in air is 320 . Estimate the diameter of the tube. One end of the tube is now closed. Calculate the lowest frequency of resonance for the tube. 5. Two speakers and , driven by the same amplifier, are placed at am and m (figure. The speakers vibrate in phase at 600 Hs. A man stands at a point on the X-axis at a very large distance from the origin and starts moving parallel to the Y-axis. The speed of sound in air is 330 m/s. (a) At what angle will the intensity of sound drop to a minimum for the first time? (b) At what angle will he hear a maximum of sound intensity for the first time? (c) If he continues to walk along the line, how many more maxima can be hear? 6. Two tuning forks with natural frequencies of 340 Hz each move relative to a stationary observer. One fork moves away from the observer, while the other moves towards him at the same speed. The observer hears beats of frequency 3 Hz. Find the speed of the tuning fork. The speed of sound in air = 340 . 7. A source of sound of frequency 256 Hz is moving rapidly towards a wall with a velocity of 5 . The speed of sound is 330 . How many beats per second will be heard by an observer (i) between the wall and the source ? (ii) behind the source ? (iii) moving with the source ? 8. A radar R and a detector D of radiowaves are a distance d apart on a level ground. Radiowaves coming directly from R and those reflected from a layer of ionosphere at an altitude H above the ground reach the detector D in the same phase giving rise to a high amplitude radio signal. When the layer rises up a distance h, no signal is detected at D. If the incident and reflected waves make the same angle with the reflecting layer, find an expression on the wavelength of radiowaves in terms of d, H and h. 9. A string of length 1 m fixed at one end and on the other end a block of mass M = 4 kg is suspended. The string is set into vibrating and represented by equation . where and are in cm and is in seconds. (a) Find the number of loops formed in the string . (b) Find the maximum displacement of a point at cm (c) Calculate the maximum kinetic energy of the string (d) Write down the equations of the component waves whose superposition gives the wave 10. At two points and on a liquid surface two coherent wave sources are set in motion with the same phase. The speed of the waves in the liquid ms-1, the frequency of vibration Hz and the amplitude m. At a point of the liquid surface which is at a distance m from and m from a piece of cork floats (i) Find the displacement of the cork at . (ii) Find the time that elapses from the moment the eave sources were set in motion until the moment that the cork passes through equilibrium position for the first time. PROBLEMS 1. A band playing music at a frequency f is moving towards a wall at a speed . A motorist is following the band with a speed . If is the speed of sound, obtain an expression for the beat frequency heard by the motorist. The air column in a pipe closed at one end is made to vibrate in its second overtone by a tuning fork of frequency 440 Hz. The speed of sound in air is 330 . End corrections may be neglected. Let denote the mean pressure at any point in the pipe, and the maximum amplitude of pressure variation. (a) Find the length L of the air column. (b) What is the amplitude of pressure variation at the middle of the column? (c) What is the maximum and minimum pressure at the open-end of the pipe? (d) What is the maximum and minimum pressure at the closed-end of the pipe? 2. A long wire PQR is made by joining two wires PQ and QR of equal radii. PQ has length 4.8 m and mass 0.06 kg. QR has length 2.56 m and mass 0.2 kg. The wire PQR is under a tension of 80 N. A sinusoidal wave-pulse of amplitude 3.5 cm is sent along the wire PQ from the end P. No. power is dissipated during the propagation of the wave-pulse. Calculate : (a) The time taken by the wave-pulse to reach the other end R of the wire, and (b) The amplitude of the reflected and transmitted wave-pulse after the incident wave pulse cross the joint Q. 3. A boat is traveling in a river with a speed of 10 m/s along the stream flowing with a speed of 2 m/s. From this boat, a sound transmitter is lowered into the river through a rigid support. The wavelength of the sound emitted from the transmitter inside the water is 14.45 mm. Assume that attenuation of sound in water and air is negligible. (a) What will be the frequency detected by receiver kept inside the river downstream? (b) The transmitter and the receiver are now pulled up into the air. The air is blowing with a speed of 5 m/s in the direction opposite the river stream. Determine the frequency of the sound detected by the receiver. (Temperature of the air and water = 20ºC; Density of river water = 103 kg/m3;Bulk modulus of the water Gas constant R = 8.31 J/mol-K; Mean molar mass of air for air = 1.4. 5. Two narrow cylindrical pipes and have the same length. Pipe is open at both ends and is filled with a monatomic gas of molar mass . Pipe is open at one end and closed at the other end, and is filled with a diatomic gas of molar mass . Both gases are at the same temperature. (a) If the frequency to the second harmonic of the fundamental mode in pipe is equal of the frequency of the third harmonic of the fundamental mode in pipe , determine the value of . (b) Now the open end of pipe is also closed (so that the pipe is closed at both ends). Find the ratio of the fundamental frequency in pipe to that in pipe . 6. In a resonance tube experiment to determine the speed of sound in air, a pipe of diameter 5 cm is used. The air column in pipe resonates with a tuning fork of frequency 480 Hz when the minimum length of the air column is 16 cm. Find the speed of sound in air at room temperature. 7. A string of mass per unit length is clamped at both ends such that one end of the string is at and the other is at . When string vibrates in fundamental mode amplitude of the mid point of the string is , and tension in the string is . Find the total oscillation energy stored in the string. ANSWERS OBJECTIVE ASSIGNEMENTS LEVEL – I 1. (c) 2. (d) 3. (a) 4. (b) 5. (b) 6. (a) 7. (b) 8. (d) 9. (d) 10. (c) 11. (d) 12. (b) 13. (d) 14. (a) 15. (a) LEVEL – II 1. (b) 2. (a) 3. (c) 4. (a) 5. (b) 6. (a) 7. (a) 8. (c) 9. (b) 10. (a) 11. (a) 12. (c) 13. (a) 14. (b) 15. (a) SUBJECTIVE ASSIGNMENTS LEVEL - I 1. N 2. (a) mm (b) 7.85 cm (c) , Hz displacement zero. 3. 4. Kms-1 5. First harmonic, No. 6. 346.8 ms-1 7. Hz 8. 47.2 Hz 9. (i) (a) 412.1 Hz (b) 388.6 Hz (ii) 340 ms-1 in each case 10. (i) 20 ms-1, from right to left (ii) 3.0 cm, 5.7 Hz (iii) (iv) 3.5 m. 11. (i) 6.4 rad (ii) rad (iii) rad (iv) rad. 12. (i) (a) cms-1 (b) 0.2 cms-1 (ii) (a) 0 cms-2 (b) 103 cms-2. 13. 1/1000 s. 14. First harmonic. 15. 515 Hz, 0.68 m. SUBJECTIVE ASSIGNMENTS LEVEL - II 1. Hz 2. 70 Hz 3. cm, cm, cm. 4. 180 Hz 5. Hz. 6. (a) 500 Hz (b) 459 Hz (c) 500 Hz by the passenger and 458 by the person near the track 7. One beat is heard per second. 8. (a) (b) . 9. (a) m/s (b) Hz, m/s. 10. 1.178 sec., 2.04 sec, 2.634 sec etc. SUBJECTIVE ASSIGNMENTS LEVEL - III 1. (a) 300 Hz (b) 0, 10 cm, 20 cm, 30 cm (c) 30 cm (d) 20 cm, 60 m/s 2. Hz, kg/m3 3. N 4. Hz. 5. 7.9º, 1.6º, two 6. m/s 7. (i) Beat frequency = 259.9 Hz (ii) Beat frequency = 252.2 Hz (iii) Beat frequency = 263.8 Hz 8. 9. (a) 10 (b) 3 cm (c) 142.12J (d) , . 10. (a) m (b) s. PROBLEMS 1. 2. (a) (b) (c) (d) and 3. (a) (b) 2.0 cm 4. (a) (b) 5. (a) (b) 6. 336 m/s. 7.