A 24 cm long wire with a linear density of 31.5 g/m passes across the open...

A 24 cm long wire with a linear density of 31.5 g/m passes across the open end of a 102 cm long open-closed tube of air. If the wire, which is fixed at both ends, vibrates at its fundamental frequency, the sound wave it generates excites the second vibrational mode of the tube of air. Assume the speed of sound is 340 m/s. What is the fundamental frequency of the wire? What is the wave speed on the wire?

Expert Solution

the frequency in the tube is

f_{3open-closed tube} = 3v/ 4L_tube

= (3)(340m/s) / (4)(102*10^-2 m)

= 250 Hz

frequency in wire f_1wire = v_wire/ 2L_wire

250 Hz = (1/2L_wire ) ?T_s/?

T_s = ( 250 Hz)² ( 2L_wie)² ?

= ( 250 Hz)²( 2 * 0.24m)²( 0.0315 kg/m)

= 226.8 N

genius_generous answered 2 years ago

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