Chapter 12, Problem 19P

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 and has a mass of 2.00 g. The string sounds an A₄ note (440 Hz) when played. (a) Where must the player put a finger (at what distance x from the bridge) to play a D₅ note (587 Hz)? (See Figure 12.40.) For both notes, the string vibrates in its fundamental mode. (b) Without retuning, is it possible to play a G₄ note (392 Hz) on this string? Why or why not?

Figure 12.40 Problem 19.