Sound Waves Exercise -3

* Marked Questions may have more than one correct option.  Marked Questions can be used as Revision Questions. PART - I : (ADVANCED) / PROBLEMS (PREVIOUS YEARS) Paragraph for Question Nos. 1 to 3 Two plane harmonic sound waves are expressed by the equations. y1(x, t) = A cos (0.5 x – 100 t) y2(x, t) = A cos (0.46 x – 92 t) (All parameters are in MKS) : 1. How many times does an observer hear maximum intensity in one second ? (A) 4 2. (B) 10 (D) 8 (C) 192 m/s (D) 96 m/s What is the speed of the sound ? (A) 200 m/s 3. (C) 6 (B) 180 m/s At x = 0 how many times y1 + y2 is zero in one second ? (A) 192 (B) 48 (C) 100 (D) 96 Paragraph for Question Nos. 4 to 6 Intensity Two trains A and B are moving with speeds 20 m/s and 30 m/s respectively in the same direction on the same straight track, with B ahead of A. The engines are at the front ends. The engines of train A blows a long whistle. f1 f2 frequency Assume that the sound of the whistle is composed of components varying in frequency from f1 = 800 Hz to f2 = 1120 Hz, as shown in the figure. The spread in the frequency (highest frequency – lowest frequency) is 320 Hz. The speed of sound in still air is 340 m/s. 5. The distribution of the sound intensity of the whistle as observed by the passengers in train A is best represented by (A) (B) f1 f2 frequency Intensity The speed of sound of the whistle is (A) 340 m/s for passengers in A and 310 m/s for passengers in B (B) 360 m/s for passengers in A and 310 m/s for passengers in B (C) 310 m/s for passengers in A and 360 m/s for passengers in B (D) 340 m/s for passengers in both the trains Intensity 4. f1 f2 frequency (D) f1 6. f2 Intensity Intensity (C) f1 frequency The spread of frequency as observed by the passengers in train B is (A) 310 Hz (B) 330 Hz (C) 350 Hz f2 frequency (D) 290 Hz 7. 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 75 cm 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 340 m/s, the frequency n of the tuning fork in Hz is (A) 344 (B) 336 (C) 117.3 (D) 109.3 8.* A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance. Then, (A) the intensity of the sound heard at the first resonance was more than that at the second resonance (B) the prongs of the tuning fork were kept in a horizontal plane above the resonance tube (C) the amplitude of vibration of the ends of the prongs is typically around 1 cm (D) the length of the air-column at the first resonance was somewhat shorter than 1/4th of the wavelength of the sound in air. A stationary source is emitting sound at a fixed frequency f 0, which is reflected by two cars approaching 9. the source. The difference between the frequencies of sound reflected from the cars is 1.2% of f 0. What is the difference in the speeds of the cars (in km per hour) to the nearest integer ? The cars are moving at constant speeds much smaller than the speed of sound which is 330 ms–1. 10. 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 resonates 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 11. (B) 10 grams (C) 20 grams (D) 40 grams A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/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 (A) 8.50 kHz 12. (B) 8.25 kHz (C) 7.75 kHz (D) 7.50 kHz Column I shows four systems, each of the same length L, for producing standing waves. ‘ The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as f. Match each system with statements given in Column II describing the nature and wavelength of the standing waves. Column I Column II (A) Pipe closed at one end (p) Longitudinal waves (B) Pipe open at both ends (q) Transverse waves (C) Stretched wire clamped at both ends (r) f = L (D) Stretched wire clamped at both ends and at mid-point (s) f = 2L (t) f = 4L 13*. A person blows into open-end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe. (A) a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is open. (B) a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is open. (C) a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed. (D) a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed. 14. A student is performing the experiment of Resonance Column. The diameter of the column tube is 4cm. The distance frequency of the tuning fork is 512 Hz. The air temperature is 38°C in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top end of the Resonance column. When first resonance occurs, the reading of the water level in the column is (A) 14.0 (B) 15.2 (C) 16.4 (D) 17.6 15*. Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency f 1. An observer in the other vehicle hears the frequency of the whistle to be f 2. The speed of sound in still air is V. The correct statement(s) is (are) : (A) If the wind blows from the observer to the source, f 2 > f1. (B) If the wind blows from the source to the observer, f 2 > f1. (C) If the wind blows from the observer to the source, f 2 < f1. (D) If the wind blows from the source to the observer, f2 < f1. 16. A student is performing an experiment using a resonance column and a tuning fork of frequency 244s–1. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is ( 0.350  0.005 ) m, the gas in the tube is (Useful information) : 167RT = 640j1/ 2 mole–1/ 2 ; in grams are given in the options. Take the value of (A) Neon (M = 20, (C) Oxygen (M = 32, 17. 10 7 = ) 20 10 10 9 = ) 32 16 140RT = 590j1/ 2 mole–1/ 2 . The molar masses M 10 for each gas as given there.) M (B) Nitrogen (M = 28, (D) Argon (M = 36, 10 3 = ) 28 5 10 17 = ) 36 32 Four harmonic waves of equal frequencies and equal intensities 0 have phase angles 0, When they are superposed, the intensity of the resulting wave is n0. The value of n is :  2 , and . 3 3 18 A stationary source emits sound of frequency f0 = 492 Hz. The sound is reflected by a large car approaching the source with a speed of 2ms –1. The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz ? (Given that the speed of sound in air is 330 ms–1 and the car reflects the sound at the frequency it has received). 19. Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed 1.0 ms−1 and the man behind walks at a speed 2.0 ms−1. A third man is standing at a height 12 m above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency 1430 Hz. The speed of sound in air is 330 ms–1. At the instant, when the moving men are 10 m apart, the stationary man is equidistant from them. The frequency of beats in Hz, heard by the stationary man at this instant, is __________. 20*. In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true ? (A) The speed of sound determined from this experiment is 332 ms–1 (B) The end correction in this experiment is 0.9 cm (C) The wavelength of the sound wave is 66.4 cm (D) The resonance at 50.7 cm corresponds to the fundamental harmonic PART - II : (MAIN) / PROBLEMS (PREVIOUS YEARS) 1. A whistle producing sound waves of frequencies 9500 Hz and above is approaching a stationary person with speed v ms–1. The velocity of sound in air is 300 ms–1. If the person can hear frequencies upto a maximum of 10,000 Hz, the maximum value of v upto which he can hear the whistle is: (1) 30 ms–1 2. (2) 15 2 ms–1 (3) 15 ms–1 (4) 15 ms–1 2 A sound absorber attenuates the sound level by 20 dB. The intensity decreases by a factor of : (1) 1000 (2) 10000 (3) 10 (4) 100 3.  The speed of sound in oxygen (O2) at a certain temperature is 460 ms–1. The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal) : (1) 500 ms–1 (2) 650 ms–1 (3) 330 ms–1 (4) 460 ms–1 4. While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance. Then (1) x > 54 (2) 54 > x > 36 (3) 36 > x > 18 (4) 18 > x 5. A motor cycle starts from rest and accelerates along a straight path at 2 m/s 2. At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was at rest? (Speed of sound = 330 ms–1) (1) 98 m (2) 147 m (3) 196 m (4) 49 m 6. A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s. (1) 12 7. (2) 8 (3) 6 (4) 4 A train is moving on a straight track with speed 20 ms–1. It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound = 320 ms–1) close to : (1) 6% (2) 12% (3) 18% (4) 24% 8. A pipe open at both ends has 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 is now : (1) 3f 4 (2) 2f (3) f (4) f 2 9. An observer is moving with half the speed of light towards stationary microwave source emitting waves at frequency 10GHz. What is the frequency of the microwave measured by the observer ? (speed of light = 3 × 108ms–1) (1) 15.3 GHz (2) 10.1 GHz (3) 12.1 GHz (4) 17.3 GHz 10. A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 × 103 kg/m3 and its Young's modulus is 9.27 × 10 10 Pa. What will be the fundamental frequency of the longitudinal vibrations ? (1) 10kHz (2)7.5kHz (3) 5kHz (4) 2.5kHz EXERCISE-3 PART - I 1. 4. 7. 10. 12. 13. 16. 19. (A) 2. (A) 3. (C) (B) 5. (A) 6. (A) (A) 8. (AD) 9. 7 (B) 11. (A) (A) – p,t , (B) – p,s, (C) – q,s, (D) – q, r (BD) 14. (B) 15. (AB) (D) 17. 3 18. 6 5.00 20. (AC) 1. (4) 4. 7. 10. (1) (2) (3) PART - II 2. 5. 8. (4) (1) (3) 3. 6. 9. [BONUS] (3) (4)