Assignment 1 Acoustics

1. Which of the following options represent a sound source moving with speed of sound? (In the figures, green dot represents source and brown circles represent sound waves.) C A B D

2. Which of the following waves requires presence of a material medium for propagation? Light. Sound. X rays. Infrared rays.

3. Which of the following equations is nonlinear in ‘𝒚’ or ‘𝒙’ ? 𝜕𝑦 𝜕𝑡 =2 𝜕𝑥 𝜕𝑡 + 3 . 𝜕 4 𝑦 𝜕 𝑡 4 =2 𝜕 4 𝑥 𝜕 𝑡 4 + 3 . 𝜕𝑦 𝜕𝑡 2 =2 𝜕 2 𝑥 𝜕 𝑡 2 + 3 . 𝑦=7𝑥+9 .

4. Consider a differential equation, 𝒗 𝒊 =𝑹𝑪 𝒅 𝒗 𝒄 𝒅𝒕 + 𝒗 𝒄 4. Consider a differential equation, 𝒗 𝒊 =𝑹𝑪 𝒅 𝒗 𝒄 𝒅𝒕 + 𝒗 𝒄 . Here, 𝒗 𝒄 and 𝒗 𝒊 are functions of time and all other terms are constant. Which of the following statements is true about homogeneous and particular response of the system represented by above differential equation? Homogeneous response decays with time and particular response gives steady state solution. Both homogeneous and particular responses decay with time. Both homogeneous and particular responses grow with time. Homogeneous response gives steady state solution and particular response decays with time.

5. Consider a signal, 𝒙 𝒕 =𝑹𝒆 𝑨 𝒆 𝝅 𝟒 +𝑩−𝒋𝑪 𝒋 𝒕 5. Consider a signal, 𝒙 𝒕 =𝑹𝒆 𝑨 𝒆 𝝅 𝟒 +𝑩−𝒋𝑪 𝒋 𝒕 . What can we conclude about decay or growth of 𝒙(𝒕) ? (A,B and C are positive constants) 𝑥 𝑡 will decay with rate of decay B. 𝑥 𝑡 will grow with rate of growth B. 𝑥 𝑡 will decay with rate of decay C. 𝑥 𝑡 will grow with rate of growth C.

6. Which of the following systems decays fastest? Under damped system. Critically damped system. Over damped system. Both over damped and underdamped.

7. Which of the following statements is not true about Bode plots? Help to study linear systems. They are plots of the time response of a linear system. Shows asymptotic behavior of a transfer function. Not used for nonlinear systems

8. Which of the following is true about the axes for Bode phase plots? x-axis y-axis a) b) c) d)

9. Which physical quantity is used to characterize sound pressure level in dB? Amplitude of pressure produced due to pressure wave, radiated to atmosphere with rest pressure Po. Amplitude of absolute pressure in atmosphere when sound is produced. RMS value of pressure produced due to pressure wave radiated to atmosphere with rest pressure Po. RMS value of absolute pressure produced in atmosphere when sound is produced.

10. Which of the following options is not required for deriving the 1-D Wave Equation? Newton’s 2nd law of motion. Conservation of mass. Equilibrium of moment. Gas law.

11. The linearized equation of momentum for 1D wave propagation is_______? 𝜕𝑝 𝜕𝑥 = 𝜌 𝑜 𝜕𝑢 𝜕𝑡 . 𝜕𝑝 𝜕𝑥 = −𝜌 𝑜 𝜕𝑢 𝜕𝑡 . 𝜕𝑢 𝜕𝑥 = 𝜌 𝑜 𝜕𝑝 𝜕𝑡 . 𝜕𝑢 𝜕𝑥 = −𝜌 𝑜 𝜕𝑝 𝜕𝑡 .

12. Which of the following thermodynamic processes accurately captures the behavior of gas when an acoustic wave passes through it? Isobaric process. Isochoric process. Isothermal process. Adiabatic process.

13. _____ is the expression for speed of sound in fluids? 𝑐= 𝛾 𝑝 𝑜 𝜌 𝑜 . 𝑐= 𝑝 𝑜 𝛾𝜌 𝑜 . 𝑐= 𝛾 𝑝 𝑜 2 𝜌 𝑜 . 𝑐= 2 𝑝 𝑜 𝛾 𝜌 𝑜 .

14. Which of the following options can be a suitable solution for the wave equation, 𝝏 𝟐 𝒑 𝝏 𝒙 𝟐 = 𝟏 𝒄 𝟐 𝝏 𝟐 𝒑 𝝏 𝒕 𝟐 ? 𝑓 𝑡− 𝑥 𝑐 . 𝑓(𝑡+ 𝑥 𝑐 ). Both a) and b). None of the above.

15. Which of the following statements can be made for an infinitely long tube excited by a piston, for the position x=0? P+ = P- P+ = -P- P- = 0 P+ = 0 x=0

16. Which of the following relations explicitly shows that ‘c’ represents the speed of sound wave? 𝜕 2 𝑝 𝜕 𝑥 2 = 1 𝑐 2 𝜕 2 𝑝 𝜕 𝑡 2 𝑐= 𝛾 𝑝 𝑜 𝜌 𝑜 𝑐= 𝑝 𝑜 𝛾𝜌 𝑜 𝑝 𝑥,𝑡 =𝑓 𝑡− 𝑥 𝑐 +𝑓 𝑡+ 𝑥 𝑐

17. Which of the following is the transmission line equation for 1-D planar sound waves propagating in loss-less medium? 𝑝(𝑥,𝑡) 𝑢(𝑥,𝑡) = 𝑃 + 𝑃 − 𝑃 + 𝑧 𝑜 𝑃 − 𝑧 𝑜 𝑒 − 𝑠𝑥 𝑐 𝑒 𝑠𝑥 𝑐 𝑒 𝑠𝑡 𝑝(𝑥,𝑡) 𝑢(𝑥,𝑡) = 𝑃 + 𝑃 − 𝑃 + 𝑧 𝑜 − 𝑃 − 𝑧 𝑜 𝑒 − 𝑠𝑥 𝑐 𝑒 𝑠𝑥 𝑐 𝑒 𝑠𝑡 𝑝(𝑥,𝑡) 𝑢(𝑥,𝑡) = 𝑃 + − 𝑃 − 𝑃 + 𝑧 𝑜 𝑃 − 𝑧 𝑜 𝑒 − 𝑠𝑥 𝑐 𝑒 𝑠𝑥 𝑐 𝑒 𝑠𝑡 𝑝(𝑥,𝑡) 𝑢(𝑥,𝑡) = 𝑃 + − 𝑃 − 𝑃 + 𝑧 𝑜 − 𝑃 − 𝑧 𝑜 × 𝑒 − 𝑠𝑥 𝑐 𝑒 𝑠𝑥 𝑐 × 𝑒 𝑠𝑡

18. Which of the following acoustical property varies with position in a medium? Driving point impedance Specific acoustic impedance Characteristic impedance Options ‘a’ and ‘b’

19. Which of the following instruments can be used for characterizing acoustic properties of a material? Kundt’s tube. Seismometer. Muffler. Accelerometer.

20. The definition of standing wave ratio(𝝆) is: 𝜌= 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 𝜌= 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 𝜌= 2×𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 𝜌= 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 2×𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒

21. If the Which of the following is the appropriate statement about the velocity of sound derived by assuming adiabatic and isothermal processes? Velocity of sound derived with adiabatic process is higher than that of isothermal process. Velocity of sound derived with adiabatic process is lower than that of isothermal process. Velocity of sound derived with adiabatic process is equal to that of isothermal process. Velocity of sound derived with adiabatic process may be higher or lower than that of isothermal process.

Cross sectional Area = Ao 22. A cylinder-piston arrangement is at its equilibrium position. If we give a small disturbance to piston, the gas in the cylinder will act as spring. What will be the expression for the spring stiffness of such a spring? Assume that the volume of gas in the cylinder, when the piston is in equilibrium is 𝑽𝑶. Volume = Vo Cross sectional Area = Ao Piston Cylinder 𝐾= 𝑑𝑝 𝑑𝑉 𝑉 𝑜 2 𝐾= 𝑑𝑝 𝑑𝑉 𝐴 2 𝐾= 𝑑𝑝 𝑑𝑉 𝐴 −2 𝐾= 𝑑𝑝 𝑑𝑉 𝑉 𝑜 −2

23. Two long metallic plates are kept in parallel and the potential difference across them is 𝑽 𝒕 . What is the boundary condition at x=0? 𝑥=0 𝑥= -𝑙 𝑉(𝑡) ~ At 𝑥=0, current = ∞ At 𝑥=0, current = 0 At 𝑥=−𝑙, current = ∞ At 𝑥=−𝑙, current = 0

24. A sound wave with an incident complex magnitude 𝑷 + enters another medium. The complex magnitude for reflected and transmitted sound waves is 𝑷 − and 𝑷 𝐓 , respectively. What is the attenuation factor for such a wave as it enters into the second medium?? 𝑃 𝑇 𝑃 + 𝑃 𝑇 𝑃 + 2 𝑃 𝑇 𝑃 + 1 2 𝑃 𝑇 𝑃 + −2 𝑃 + 𝑃 𝑇 𝑃 − Medium 1 Medium 2

25. What is the definition for transmission loss (𝑻𝑳), for a sound wave propagating from one medium into another? 𝑇𝐿=10 log 10 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝑤𝑎𝑣𝑒 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑 𝑤𝑎𝑣𝑒 𝑇𝐿=−10 log 10 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝑤𝑎𝑣𝑒 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑 𝑤𝑎𝑣𝑒 𝑇𝐿=20 log 10 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝑤𝑎𝑣𝑒 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑 𝑤𝑎𝑣𝑒 𝑇𝐿=−20 log 10 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝑤𝑎𝑣𝑒 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑 𝑤𝑎𝑣𝑒

Average transmission loss (dB) 26. The following graph depicts transmission loss for a planar wall with respect to varying frequency. In this graph, which region is “mass controlled”? A B Average transmission loss (dB) Frequency (Hz) A B Both A and B None of the above

27. In stiffness controlled region , expression for attenuation for an acoustic wave incident from random direction ‘𝜽’ is given by _________? 1 1+ cos 𝜃 2 𝑍 𝑜 𝑐𝜔 2 1 1+ sin 𝜃 2 𝑍 𝑜 𝑐𝜔 2 1 1+ 1 2 𝑍 𝑜 𝑐𝜔 2 1 1+ 1 2 𝑍 𝑜 𝑐𝜔

28. The value of incident and transmitted sound power intensity on a plane wall of thickness 30 cm is 130 dB and 80 dB, respectively. Thus, the reduction of sound intensity across the wall is by a factor of ____ . 10000 100000 1000 100

29. If for an ISO frequency band the central frequency is p, then it’s band number would be : 20log10 𝑝 40log10 𝑝 10log10 𝑝 None of above

30. Acoustical average power per cycle is not zero for: An undamped infinitely long tube. A short undamped open tube. A short undamped close tube. None of the above.

31. If power correction factor for a system is 1, then it’s transmission loss will be _________. Maximum Minimum Infinite None of above

32. For a monopole sound source which of the following is true. 𝜕𝑝 𝜕𝑟 = 0; 𝜕𝑝 𝜕θ = 0 and 𝜕𝑝 𝜕φ ≠ 0 𝜕𝑝 𝜕𝑟 = 0; 𝜕𝑝 𝜕θ ≠ 0 and 𝜕𝑝 𝜕φ = 0 𝜕𝑝 𝜕𝑟 ≠ 0; 𝜕𝑝 𝜕θ = 0 and 𝜕𝑝 𝜕φ = 0 None of above Note: p= Pressure r = Radial direction θ = Azimuthal angle φ=Zenith angle

33. The magnitude of pressure at point P, which is at a distance r from a simple monopole sound source is proportional to _________. 𝑟 1 𝑟 1 𝑟 2 1 𝑟

34. The value of specific acoustical impedance, Z(r,ω) for a monopole sound source becomes approximately equal to the characteristic impedance, Z0, of the medium at a radial distance, r, when ____. r≫ λ 2π r≪ λ 2π Never None of the above

35. Volume velocity of a sound source is defined as: Dot product of pressure of sound source and velocity of sound source. Dot product of velocity of sound source and area of sound source. Dot product of pressure of sound source and area of sound source. None of the above

36. Near-field for a monopole sound source refers to the zone for which the radial distance (r) is in the range of ____. 0 to 2 times ( λ 2π ) 0 to 3 times ( λ 2π ) 0 to 4 times ( λ 2π ) 0 to 5 times ( λ 2π )

37. At a particular angular position P, two monopole sound sources separated by a distance of 𝝀 𝟒 produce minimum pressure amplitude. If the magnitude of volume velocity of both of these sources is same, and the phase difference their volume velocities is π/2 radians, then, what will be the angular position of point P. 0 degree 90 degree 180 degree 270 degree

38. The ratio of specific characteristic impedance for a spherical and planar wave fronts, i.e. 𝒁 𝒓𝒂𝒅𝒊𝒂𝒍 𝒁 𝒑𝒍𝒂𝒏𝒂𝒓 is: 1 1+ ( λ 2π𝑟 ) 2 1 1+ ( λ π𝑟 ) 2 1 1+ ( λ 4π𝑟 ) 2 None of above

39. A small spherical sound dissipates 12 W of acoustical power 39. A small spherical sound dissipates 12 W of acoustical power. Calculate the sound intensity level in air at a point, which is 70 cm away from the sound source. Assume free-field conditions. 100 dB 122 dB 136 dB 146 dB

40. The relation for volume-velocity for a monopole sound source is: Volume-velocity = ____. 4𝜋𝑟 𝑝(𝑟,𝜔) 3𝑗 𝜔 𝜌 𝑒 −( 𝑗𝜔𝑟 𝑐 ) 4𝜋 𝑝(𝑟,𝜔) 𝑗 𝜔 𝑟 𝜌 𝑒 −( 𝑗𝜔𝑟 𝑐 ) 4𝜋𝑟 𝑝(𝑟,𝜔) 𝑗 𝜔 𝜌 𝑒 −( 𝑗𝜔𝑟 𝑐 ) None of above

41. Calculate the sound pressure level for the following signal. The medium of propagation is air at STP. 105 dB 104 dB 103 dB 102 dB