You have two strings of length 0.5 m. Both strings are fixed at both ends and ha

Question

You have two strings of length 0.5 m. Both strings are fixed at both ends and have tension 10 N. The first string has a mass of 0.5 kg and the second has a mass of 2.5 kg. You also have two tubes. The first is open at both ends and the second is open at one end and closed at the other end. The tubes have the same length as the strings: 0.5 m. For each string and tube, calculate the wavelength and frequency of the fundamental resonance and the next resonance (which has a shorter wavelength). Draw the wavelengths for each. Assume the tubes are in 20

Explanation / Answer

apply the formula for fundamental frequency f = (1/2L)* sqrt(T/u)

where T is tension

and u is ,mass per unit length u = m/L = 2.5/0.5 = 5 kg/m

f = (1/(2 * 0.5)) * ( sqrt(10/5))

f = 1.414 Hz is the frequency of each string

so

next higher wavelengths are

f2 = 2f1 = 2* 1.414 = 2.828 Hz

f3 = 3f1 = 3* 1.414 = 4.242 Hz

f4 = 4 f1 = 4* 1.414 = 5.656 Hz

--------------------------

wavelength L = 2lf = 2* 0.5 *1.414 = 1.414 m/s

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