Math 5: Music and Sound. Some midterm practise questionsYou will be provided with the equations on the back sheet but no othersThere are other formulaeThe first two questions in HW5 are good rev iew too.1. compare the Pythagore an semitone 256/ 243 to the equal-tempere d version.2. compute the frequency of C8 the highest note on the piano.3. How many major thirds should fit in an octave? A just-tuned major third is 5:4. Find the frequencyerror in cents in constructing an octave using this interval. How is this res olved in music practice?4. What is the ‘missing fundamental’ illusion?5. What is the amplitude and phase of the signal√3 sin(500πt) + cos(500πt) ?6. An orchestra radiates 1 0 W acous tic p ower in all directions. Find the intensity in dB at a distance 20meters. How much power would your ear with area 5 cm2= 0.0005 m2collect at this distance?7. Two drummers hit notes one every 0 .3 s and the other every 1.6 s (this is ac tua lly a syncopated rhythmsimilar to rhumba clave). They start together. What is the period of their joint sound?8. What ‘strike note’ will you perceive if a b e ll has partials 210, 230, 991, 1320, 1649, 1984, 5775 Hz?9. Compare the diss onance of the pair of periodic signals at frequencies 400 and 600 Hz to the pair at 400and 750 Hz, using our usual rule (within 10% but not within 15 Hz). Assume par tia ls are only relevantup to 2400 Hz. What are these two musical intervals? (give error from equal-tempe red intervals)10. Explain the following terms (to someone not in this course)(a) Fourier series(b) intensity(c) wavelength(d) pa rtial11. How fast would a police car need to be traveling so that as they drove away from you their siren wasa perfect forth lower than its pitch when stationary?12. Draw a spacetime diagram illustrating how we measured the speed of sound outside using echoes.13. Explain how the phon measure of loudness differs from the decibel. If your ear is more sensitive at4000 Hz than at 1000 Hz, is the phons greater or less than the dB at 4000 Hz?14. What is the Shepard’s tones illusion, how does it work, and what does it pr ove about our perceptionof pitch?1Useful informationω = 2πfc = fλdB = 10 log10I10−12W/m2Q = πτTfobsf=11 − v/cor 1 + v/csin(a + b) = sin a cos b + cos a sin bsin a + sin b = 2 cos(a − b2) sin(a + b2)Intervals by number of semitones:1. minor s e c ond2. whole tone (major second)3. minor third4. major third5. per fect fo urth6. tritone (augmented fourth)7. per fect fifth8. minor s ix th9. major sixth10. minor seventh11. major seventh12. octaveThe standard musical pitch A4 is 440 HzYou can use the speed of sound as 340