The portion of string between the bridge and upper end of the fingerboard (the part of the string that is free to vibrate) of a certain musical instrument is 60.0 cm long [.6m] and has a mass of 2.23 g [.00223kg]. The string sounds an A4 note (440 Hz) when played.

Where must the player put a finger (at what distance from the bridge) to play a D5 note (587 Hz)? For both notes, the string vibrates in its fundamental mode.
x= ?? cm

Without retuning, is it possible to play a G4 note (392 Hz) on this string?

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  1. On the A4 note, you know length and frequency. Assume it is in half wave resonacne, so wavelength is twice length. Use the wave equation (f*lambda=velocity) to find velocity.

    Then, solve for wavelength on the D5 note, and L must be half that.

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