viewnotes/183/VTU SYLLABUS 2010 STRENGTH OF MATERIALS COMMON TO CVTREVCTM 10CV33 Engineering

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A sonometer wire of length 1.5 m is made of steel. The tension in it produce an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are 7.7 × 103 kg / m3 and 2.2 × 1011 N/m2 respectively ? - physics 2013

 (1) 188.5 Hz
 (2) 178.2 Hz
 (3) 200.5 Hz
 (4) 770 Hz 


By:milan-ransingh

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Transverse waves on a Sonometer wire/bridge . Young's modulus Y = Stress / Strain = 2.2 * 10^11 N/m²    Stress = Tension / Cross section area = T / A    Strain = 1 % = 0.01    2.2 * 10^11 =  (T / A ) / 0.01 =  T / (0.01 A)       T = 2.2 * 10^9 * A    Newtons   L = 1.5 meter     Volume density d =  7.7 * 10³  kg/m³     Linear density μ = volume density * Area = d * A = 7.7 * 10³ * A  kg /meter   velocity of transverse wave on the Sonometer wire = √(T/μ)          v   = √(2.2*10^9 / 7.7*10³)  m/sec             = 534.52 m/sec   Fundamental note has a wavelength = λ = 2 * L = 3 meters.  As the given wire vibrates with one loop.  Nodes at both ends and anti-node at the center.  So half of the wavelength is equal to the length of the wire.       
So frequency = v / λ = 178.17 Hz
(2) 178.2 Hz

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