A steel wire with mass 29.9 g and length 1.24 m is strung on a bass so that the

Question

A steel wire with mass 29.9 g and length 1.24 m is strung on a bass so that the distance from the nut to the bridge is 1.10 m. (a) Compute the linear density of the string. k/m2 (b) What velocity wave on the string will produce the desired fundamental frequency of the E1 string, 36.92 Hz? m/s (c) Calculate the tension required to obtain the proper frequency. N (d) Calculate the wavelength of the string's vibration. m (e) What is the wavelength of the sound produced in air? (Assume the speed of sound in air is 343 m/s.) m

Explanation / Answer

v = sqrt(F/mu) = 192.7 m/s. Without the picture, I can't determine the wavelength, but it is dependent on how many nodes are in the standing wave pattern between the ends of the string. If n is the number of nodes between the ends, then the wavelength will be 2L/(n+1), where L is the length of the string. Once you know velocity and wavelength, frequency is given by v = lambda*f.

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