The portion of a cello string between the bridge and upper end of the fingerboard (that part of the string that is free to vibrate) is of length 60.0 cm, and this length of the string has mass 2.00 g. The string sounds an A4 note (440 Hz) when played.
Where must the cellist put a finger (what distance x from bridge) to play a D5 note (587 Hz)? For both notes, the string vibrates in its fundamental mode.

Explanation:

length of vibration l = .6 m

mass per unit length m = 2 x 10⁻³ / .6

= 3.33 x 10⁻³ kg/ m

n =

n is frequency of vibration , l is length , T is tension in the string .

Apply this formula in the first case

440 =

Apply this formula for second case

n =

587 =

Dividing

=

l = .45 m .

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