Question

3 A violin and a flute play together; the combined pressure us. time graph is shown below. 19 16 14 12 10 8 6 4 2 0 2400 2800 2600 3000 3200 3600 3400 3800 4000 4200 4400 4600 4800 t (ms) What can you tell about the frequencies of the instruments from this information? What can't you tell? The lute player says to the violinist: "hey, you're flat!" If the flute is playing a 587 Hz sound. what can you tell about the violin's sound? How long would they have to play together in order for you to hear 55 beats? 10

Answer 1

(1) As shown from the graph, maximum and minimum pressure waves produces at regular intervals of time means Beats are produces Time interval between maximum and minimum pressure waves are T=500ms Beat frequency (Af)= = sooms (1970) = 2.0Hz We can tell beat frequencies exactly tell 2.0 Hz, not exactly tell the original frequencies (or)natural frequencies of both the sound waves (2) Consider 11, are the frequencies of the waves from the given data, Af=2.0Hz Wi-|(or) 1- fil= 2.0 Hz 1587 Hz – Ba|(or) - 587 Hz|= 2.0 Hz fa = 589 Hz (or) 585 Hz.violin frequency (3)Time taken by both are together in order to produce 55 beats are, t = 557 = 5$ sooms (10 = 27.58 (4) Frequency is inversely proportional to length of strir Tighten string produces a higher frequency of sound than looser one, but Tighten (or)looses the violin string does not effect] the beat times or beat frequency as there is combination of music from both violin and flute at all times as evidance in the presure graph.

(5) We can not exactly tell the original frequencies (or)natural frequencies of both the sound waves and impossible to tell the percentage increase (or) decrease in tension for tuning (6) Using relation between fundamental frequency of flute (the), velocity of sound in air, to calcuate wavelength of sound waves in the string wa (here vi at room temperature 343m/s ) 21 = (here 2=21) 1 343m/s ] 1= 587 Hz = 0.29m (or) 29 cm Frequency of tuning (flute) in the stretched atring is, Rearange the above equation for linear density of the string. 4- 41" frame 65N 4(0.29m)" (587Hz) $ 0.33kg/m