If look inside a real piano , you'll see that the assumption made in part (b) of Illustration 7.31 is only partially true . The strings are not likely to have the length of the A string is only 64 % of the length of the C string . What is theratio of their tensions ?

If look inside a real piano , you'll see that the assumption made in p

1.	If look inside a real piano , you'll see that the assumption made in part (b) of Illustration 7.31 is only partially true . The strings are not likely to have the length of the A string is only 64 % of the length of the C string . What is theratio of their tensions ?
Answer» Solution :The ratio of frequencies : `( f_(1) A)/( f_(1) C) = (L_(C ))/(L_(A)) sqrt (( T_(A))/( T_(C)))` `(T_(A))/(T_( C)) = ((L_(A))/(L_(C )))^(2) ((f_(1) A)/( f_(1) C))^(2)` `(T_(A))/( T_( C )) = ( 0.64)^(2) (( 440)/( 262))^(2) = 1.16` NOTICE that this result REPRESENTS only a `16 %` increase in tension , compares with the `18.2%` increase in PART (b) of Illustration 7.31.