Question

A particularly beautiful note reaching your ear from a rare Stradivarius violin has a wavelength of 39.1 cm. The room is slightly warm, so the speed of sound is 344 m/s.

If the string's linear density is 0.720 g/m and the tension is 140 N , how long is the vibrating section of the violin string?

Note: pleae provide the answer with real mathmatical symboles, not merely keybored parenthesis and slashes.

Answer 1

frequency of the note is f = v/lamda = 344/0.391 = 880 Hz

then using f = (1/2l)*sqrt(T/mu)

l is the required length of the string

T is the tension in the string = 140 N

mu is the linear density = 0.720*10^-3 kg/m

then length of the string is l = (1/2f)*sqrt(T/mu)

l = (1/(2*880))*sqrt(140/(0.720*10^-3)) = 0.2505 m = 25.05 cm