Waves and sound-03-OBJECTIVE SOLVED

SOLVED OBJECTIVE PROBLEMS Problem 1. The amplitude of a wave disturbance propagating in the positive x–direction is given by at t = 0 and at , where x and y are in meter. Assuming that the shape of the wave disturbance does not change during the propagation, the speed of the wave is (a) 0.5 m/s (b) 1 m/s (c) 1.5 m/s (d) 2 m/s. Solution : At , or At or, or, Speed of the wave Alternative solution: The given pulse is represented by where v is the velocity of the wave. At it is given that and At , or Ans. (a) Problem 2. A note has a frequency of 128 Hz. The frequency of a note which is two octave higher than this is (a) 256 Hz (b) 320 Hz (c) 400 Hz (d) none of these. Solution : One octave higher means the note whose frequency is 2 times the given frequency . Similarly 2 octave higher means 3 times the given frequency , which is Ans. (d) Problem 3. The third overtone of a closed pipe is observed to be in unision with the second overtone of an open pipe. The ratio of the lengths of the pipes is (a) (b) (c) 7/4 (d) 7/6. Solution : Frequency of the fundamental note in closed pipe is . Only the odd harmonics, (first overtone) (second overtone) (third overtone) _______________________ are present Frequency of the fundamental note in open pipe is . All the harmonics (second harmonic or first overtone) (third harmonic or second overtone) ( fourth harmonic or third overtone) ___________________________________ are present Given that : or Ans. (d) Problem 4. The speed of sound wave in a mixture of 1 mole of helium and 2 moles of oxygen at 27° C is (a) 400 m/s (b) 600 m/s (c) 800 m/s (d) 1200 m/s. Solution : The speed of sound wave is where The molecular weight of the mixture Substituting these values, we get Ans. (a) Problem 5. A traveling wave in a stretched string is described by the equation . The maximum particle velocity is (a) (b) (c) (d) Solution : Particle velocity Maximum particle velocity Ans. (a) Problem 6. The extension in a string, obeying Hooke’s law, is . The speed of sound in the stretched string is . If the extension in the string is increased to , the speed of sound will be (a) 1.22 v (b) 0.61 v (c) 1.50 v (d) 0.75 v. Solution : Tension Since or, Ans. (a) Problem 7. Two monoatomic ideal gases 1 and 2 of molecular masses and respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to that in gas 2 is given by: (a) (b) (c) (d) . Solution : Velocity of sound where is the molar mass. Ans. (b) Problem 8. The ends of a stretched wire of length are fixed at and In one experiment, the displacement of the wire is and energy is and in another experiment its displacement is and energy is . Then (a) (b) (c) (d) . Solution : In the first case frequency and in the second case frequency Energy (frequency)2 Ans. (c) Problem 9. In a wave motion can represent (a) electric field (b) magnetic field (c) displacement (d) pressure. Solution : All the options represent periodic variation in wave motion. Ans. (a, b, c and d) Problem 10. The displacement of a particle executing periodic motion is given by . This expression may be considered to be a result of the superposition of waves : (a) two (b) three (c) four (d) five. Solution : Given : = Thus the periodic motion consists of three components. Ans. (b) Problem 11. A train moves towards a stationary observer with speed 34 m/s. The train sounds 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) 18/19 (b) (c) 2 (d) 19/18. Solution : Ans. (d) Problem 12. An object of specific gravity is hung from a thin steel wire. The fundamental frequency for transverse 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 frequency in Hz is (a) (b) (c) (d) . Solution : Weight of object Buoyant force Now, where tension is provided by the weight of the object or, Ans. (a) Problem 13. 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 (a) 200 Hz (b) 300 Hz (c) 240 Hz (d) 480 Hz. Solution : Fundamental frequency of open pipe is Third harmonic of the closed pipe Given: or, Hz Ans. (a) Problem 14. The wires and of a guitar produce 4 beats per second. If the tension of is raised , then the number of beats becomes 2 per second. If the frequency of is 300, then frequency of (a) 296 (b) 298 (c) 300 (d) 294. Solution : When the tension of is raised, its frequency increase and the difference, is reduced Ans. (a) Problem 15. Two vibrating strings of the same material but length and have radii and respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length with frequency and the other with frequency . The ratio is given by : (a) 2 (b) 4 (c) 8 (d) 1. Solution : Fundamental frequency (since tension is same) (since the wires are of same material) Ans. (d) Problem 16. Two pulses is a stretched string whose centers are initially 8cm apart are moving towards each other as shown in the figure. The speed of each pulse is 2 cm/s. After 2 second, the total energy of the pulses will be : (a) zero (b) purely kinetic (c) purely potential (d) partly kinetic and partly potential. Solution : Under the given situation, the pulses overlap, the string occupies the equilibrium position. The potential energy will be zero but the total energy will exist in the form of purely kinetic energy . Ans. (b) Problem 17. A siren placed at a railway platform is emitting sound of frequency 5kHz. A passenger sitting in a moving train records a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train be records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train to that of train is : (a) 242/252 (b) 2 (c) 5/6 (d) 11/6. Solution : Ans. (b) Problem 18. 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 replaced by a mass , the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of is (a) 25 Kg (b) 5 Kg (c) 12.5 Kg (d) 1/25 Kg. Solution : where is the number of antinodes Here, Simplifying, we get 25 Kg Ans. (a) Problem 19. A transverse sinusoidal wave of amplitude a, wavelength and frequency is traveling on a stretched string. The maximum speed of any point on the string is where is the speed of propagation of the wave. If m and , then and are given by (a) (b) (c) Hz (d) Hz. Solution : Particle velocity Amplitude or, m Frequency Hz. Ans. (a), (c) Problem 20. The beat frequency produced by two tuning forks when sounded together is observed to be 4 Hz. One of the forks makes 384 vibrations per second. When the other fork is loaded with a small piece of wax, the beats disappear 1st. The frequency of the second tuning fork is (a) 388 Hz (b) 380 Hz (c) more than 388 Hz (d) less than 380 Hz. Solution : Since the frequency of beats in 4 Hz, the frequency of the second tuning fork will be either 384 + 4 = 388Hz, or 384 – 4 = 380 Hz. On loading , the frequency decreases. If 388 Hz be the true frequency, the beats after loading may disappear since frequency may decrease from 388 Hz to 384 Hz. The frequency 380Hz is not permissible , since if will decrease further and cannot increase to 384 Hz. Hence 388 Hz is the true frequency. Ans. (a)