Section A: 1. How far does the sound travel in air when a tuning fork of frequency 256Hz makes 64 vibrations. Vsound = 320m/s ? 2. (80m) Audible frequencies have a range of 20Hz to 20,000Hz. Express this range in terms of (a) period T (b) Wavelength λ in air (c) Angular Frequency .Vsound = 330m/s? 3. If a splash is heard 4.23s after a stone is dropped into a well 78.4m deep, nd the speed of sound in air? (340.87m/s) Section B: 1. A wave travelling along a straight is described by: y(x,t) = 0.0005 sin(80x-3t). Calculate A. Amplitude B. Angular frequency C. Frequency of oscillation D. Time period of oscillation and E. Initial phase F. Wavelength G. Also calculate the dsplacement y of the wave at a distance x = 30cm & time t = 20s? 2. The equation of a plane progressive wave is given by the equation y = 10 sin 2π (t –0.005x) where y and x are in cm and t in seconds. Calculate the amplitude, frequency, wave length and velocity of the wave. Also identify the nature of wave. 3. The wave function for a travelling wave is given as y(x,t)=(0.350m) sin (10πt-3πx+π/4) (a) What are the speed and direction of travel of the wave? (b) What is the vertical displacement of the string at t = 0, x = 0.1 m? (c) What are wavelength and frequency of the wave? C.R. Park of ce: D-773,L.G.F.,Opp. Market-2, C.R. Park, New Delhi-110019 fi fi fi M.N. of ce: E block,5/1 (L.G.F.) Malviya Nagar, New Delhi-110017, Contact: 011-40551421,41551421 4. A wave travelling along a straight is described by : y(x,t) = 0.0005 Sin(80x-3t). Calculate (a)Amplitude (b)wavelength (c)period & frequency of the wave. Also calculate the displacement y of the wave at a distance x=30cm & time t=20s? 5. A harmonically moving transverse wave on a string has a maximum particle velocity & acceleration of 3m/s & 90m/s2 respectively.Velocity of the wave is 20m/s. Section C: 1. A steel wire 0.72m long has a mass of 5g . If the wire is under a tension of 60N , what is the speed of transverse waves on the wires?[93m/s] 2. The speed of a transverse wave in a stretched string is 350m/s, when the tension in the string is 3.6kgwt. Calculate the speed of the transverse wave in the same string, if the tension in the string is changed to 4.9kgwt?[406m/s] 3. A copper wire is held at two ends by rigid supports . At 300C the wire is just taut with negligible tension. Find the speed of transverse waves in the wire at 10oC . Given [α = 1.7 x 10-5/oC , Y = 1.4 x 1011N/m2 & ρ=9 x 103kg/m3] 4. Find speed of the wave generated in the string as in the situation shown. Assume that the tension is not affected by the mass of the cord. 5. A copper wire is held at two ends by rigid supports. At 300C the wire is just taut with negligible tension. Find the speed of transverse waves in the wire at 10oC . Given [α = 1.7 x 10-5/oC , Y = 1.4 x 1011N/m2 & ρ=9 x 103kg/m3] 6. When a sound wave goes from rarer to denser medium, the quantity that remains unchanged is—————————— 7. Discuss the Newton’s formula for velocity of sound in air. What correction was applied to it by Laplace and why? C.R. Park of ce: D-773,L.G.F.,Opp. Market-2, C.R. Park, New Delhi-110019 fi fi M.N. of ce: E block,5/1 (L.G.F.) Malviya Nagar, New Delhi-110017, Contact: 011-40551421,41551421 Section D: 1. At what temperature will the speed of sound be double its value at 273K? [1092K] Q8)Speed of sound in air is 332m/s at STP . What will be its value in hydrogen at STP , if density of hydrogen at STP is 1/16th that of air? [1328m/s] 2. Find the ratio of velocity of sound in hydrogen gas to that in helium gas at the same temperature?[1.68] 3. A tuning fork of frequency 220Hz produces sound waves of wavelength 1.5m in air at STP. Calculate the increase in wavelength ,when temperature of air is 27oC? [0.07m] 4. Speed of sound in air is 332m/s at STP. What will be its value in hydrogen at STP,if density of hydrogen at STP is 1/16th that of air ? [1328m/s] 5. The ratio of densities of oxygen & nitrogen is 16:4.At what temperature, the speed of sound in oxygen will be equal to its speed in nitrogen at14oC?[55oC] Section E: 6. A harmonically moving transverse wave on a string has a maximum particle velocity & acceleration of 3m/s & 90m/s2 respectively.Velocity of the wave is 20m/s.Find the waveform Section F: 1. What should be minimum length of an open organ pipe for producing a note of 110 Hz? The speed of sound is 330 ms-1 ? 2. The length of an organ pipe open at both ends is 0.5 in Calculate the fundamental frequency of the pipe, if the velocity of sound in air be 350m/s .If one end of the pipe is closed, then what will be the fundamental frequency? 3. Find the ratio of the length of a closed pipe to that of an open pipe in order that the second overtone of the former is in unison/resonance with the fourth overtone of the latter. C.R. Park of ce: D-773,L.G.F.,Opp. Market-2, C.R. Park, New Delhi-110019 fi fi M.N. of ce: E block,5/1 (L.G.F.) Malviya Nagar, New Delhi-110017, Contact: 011-40551421,41551421 4. An open pipe is suddenly closed at one end with the result that frequency of the third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. What is the fundamental frequency of the open pipe? 5. The rst overtone of an open organ pipe beats with the rst overtone of a closed organ pipe with a beat frequency of 2.2 Hz. The fundamental frequency of the closed organ pipe is 100 Hz. Find the length of the pipes. Velocity of sound in air = 330 ms-1 6. Determine the possible harmonics in the longitudinal vibration of a rod clamped in the middle? 7. Prove that a pipe of length 2L open at both ends has same fundamental frequency as another pipe of length L closed at the other end. Also, state whether the total sound will be identical for two pipes. 8. The fundamental frequency of a closed organ pipe is equal to the rst overtone of an open organ pipe. If the length of the open pipe is 60 cm, what is the length of the closed pipe? 9. The length of a sonometer wire between two xed ends is 110cm. Where should the two bridges be placed so as to divide the wire into three segments, whose fundamental frequencies are in the ratio of 1:2:3? 10. The fundamental frequency of a closed pipe is equal to the rst overtone frequency of an open organ pipe.If the length of the open pipe is 60cm, what is the length of the closed pipe? 11. A pipe 30cm long is open at both ends . Which harmonic mode of the pipe resonates with a 1.1Khz source . Will resonance with the same source be observed if one end of the pipe is closed .Take speed of sound in air as 330m/s? 12. A guitar string is 90cm long & has a fundamental frequency of 124Hz . Where should it be pressed to produce a fundamental frequency of 186Hz? C.R. Park of ce: D-773,L.G.F.,Opp. Market-2, C.R. Park, New Delhi-110019 fi fi fi fi fi fi fi M.N. of ce: E block,5/1 (L.G.F.) Malviya Nagar, New Delhi-110017, Contact: 011-40551421,41551421 13. A 100cm long wire of mass 40g supports a mass of 1.6kg . Find the fundamental frequency of the portion of the string between the wall & the pulley? Section G: 1. Two waves y1=3Sin2πt & y2=3Sin6πt superimpose forming beats . Find beat frequency ? 2. When two tuning forks are sounded together , 20 beats were produced in 10s . On loading one the forks with wax again gives 4 beats per second . Find the frequency of other if other fork has frequency of 256Hz. What was the unknown frequency? 3. 64 tuning forks are arranged in order of increasing frequency . The frequency of the last fork is double the rst & each two consecutive forks produce 4 beats per second . Calculate the frequency of last fork? 4. Two sitar strings A & B playing note ‘Dha’ are slightly out of tune & produce beats with frequency 5Hz .The tension in B is slightly increased & beat frequency is found to decrease to 3Hz . What is the original frequency of B , if the frequency of A is 427Hz? 5. A tuning fork of unknown frequency gives 4 beats with a tuning fork of frequency 310Hz . It gives the same number of beats on ling . Find the unknown frequency? C.R. Park of ce: D-773,L.G.F.,Opp. Market-2, C.R. Park, New Delhi-110019 fi fi fi fi M.N. of ce: E block,5/1 (L.G.F.) Malviya Nagar, New Delhi-110017, Contact: 011-40551421,41551421 C.R. Park of ce: D-773,L.G.F.,Opp. Market-2, C.R. Park, New Delhi-110019 fi fi M.N. of ce: E block,5/1 (L.G.F.) Malviya Nagar, New Delhi-110017, Contact: 011-40551421,41551421 C.R. Park of ce: D-773,L.G.F.,Opp. Market-2, C.R. Park, New Delhi-110019 fi fi M.N. of ce: E block,5/1 (L.G.F.) Malviya Nagar, New Delhi-110017, Contact: 011-40551421,41551421
