When a violinist pulls the bow across a string, the force with which the bow is

Question

When a violinist pulls the bow across a string, the force with which the bow is pulled is fairly small, about 0.65 N. Suppose the bow travels across the A string, which vibrates at 440 Hz, at 0.45 m/s. A listener 34 m from the performer hears a sound of 57-dB intensity. Assuming that the sound radiates uniformly in all directions, with what efficiency is the mechanical energy of bowing converted to sound energy?

_______%

Explanation / Answer

=>Pin =FV =0.65*0.45 =0.2925 W =>A =4pir^2 =4pi*34^2 =14526.7 m^2 =>I =10log(Io/10^-12) =>57 =10 log(Io/10^-12) =>Io=5.01*10^-7 =>Pout =IoA =5.01*10^-7*14526.7 =>Pout =7.28*10^-3 W =>efficency n =Pout/Pin =7.28*10^-3/0.2925 =>n=2.49 %

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