Simple Nature - Light and Matter

10 Singing that is off-pitch by more than about 1% sounds bad.How fast would a singer have to be moving relative to a the rest ofa band to make this much of a change in pitch due to the Dopplereffect?11 Light travels faster in warmer air. Use this fact to explainthe formation of a mirage appearing like the shiny surface of a poolof water when there is a layer of hot air above a road.12 (a) Compute the amplitude of light that is reflected backinto air at an air-water interface, relative to the amplitude of theincident wave. Assume that the light arrives in the direction directlyperpendicular to the surface.The speeds of light in air and water are3.0 × 10 8 and 2.2 × 10 8 m/s, respectively.(b) Find the energy of the reflected wave as a fraction of the incidentenergy. ⊲ Hint, p. 920 √13 A concert flute produces its lowest note, at about 262 Hz,when half of a wavelength fits inside its tube. Compute the lengthof the flute. ⊲ Answer, p. 93014 (a) A good tenor saxophone player can play all of the followingnotes without changing her fingering, simply by altering thetightness of her lips: E♭ (150 Hz), E♭ (300 Hz), B♭ (450 Hz), andE♭ (600 Hz). How is this possible? (I’m not asking you to analyzethe coupling between the lips, the reed, the mouthpiece, and the aircolumn, which is very complicated.)(b) Some saxophone players are known for their ability to use thistechnique to play “freak notes,” i.e., notes above the normal rangeof the instrument. Why isn’t it possible to play notes below thenormal range using this technique?15 The table gives the frequencies of the notes that make upthe key of F major, starting from middle C and going up throughall seven notes.(a) Calculate the first four or five harmonics of C and G, and determinewhether these two notes will be consonant or dissonant.(b) Do the same for C and B♭. (Recall that harmonics that differby about 1-10% cause dissonance.)C 261.6 HzD 293.7E 329.6F 349.2G 392.0A 440.0B♭ 466.2Problem 15.Problems 379