A 25 cm long wire, with a linear density of 20 g/m passes across the open end of

Question

A 25 cm long wire, with a linear density of 20 g/m passes across the open end of an 85 cm long tube with one end open, one closed (as shown in the figure below). If the wire, which is fixed at both ends, vibrates at its fundamental frequency, the sound wave it generates excited the second (possible) vibrational mode of the tube of air. Assume the speed of sound in the air v = 343 m/s A) Determine the wavelength of the standing wave in the tube. [3 points] B) Determine the frequency of the wave in the tube. [2 points] C) Determine the tension on the string. [5 points]

give workings please this is for practice for a final exam

Explanation / Answer

for a closed tube, the possible wavelength are 4L, 4L/3, 4L/5, etc etc

so in your case:

(A) wavelength = 4L/3 = 113.3 cm = 1.133 m

(B) freq = speed / wavelength = 343 / 1.133 = 302.74 Hz

(C) wavelength on string = 2L = 50 cm = 0.50 m

speed of wave on string = wavelength * freq = 302.74 * 0.50 = 151.37 m/s

speed^2 = tension / linear mass density

151.37^2 = tension / 0.020 kg/m

tension = 458.2 Newtons

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