3. The speed of longitudinal waves in a thin rod is VY/p, where Y is the Young\'

Question

3. The speed of longitudinal waves in a thin rod is VY/p, where Y is the Young's Modulus in N/mº, which is a material property that measures how difficult it is to stretch the material, and p is the material's mass density in kg/m°. Calculate this sound speed in a thin steel rod, using the data below. Does sound travels faster in steel or air? Material Young's Modulus Y (N/m2) Aluminum 6.5x1010-7.5x1010 Steel | 2.0x1011 - 2.5x1011 Polycarbonate 2.0x109 – 2.4x10° Mass Density (kg/m3) 2700 7880 1220

Explanation / Answer

Since the range of Y is given, average value of Y will be used I.e. (2+2.5/2)*10^11 = 2.25*10^11

Since sound waves are longitudinal, above given relation Will be used for finding speed, v= (Y/)^1/2= ( 2.25*10^11 / 7880 )^1/2= 5343.53m/s. So, using the given data, sound speed in a thin steel rod= 5343.53m/s

As is known, speed of sound in air is 343m/s, and 5343m/s>343sm/s ; so sound travels faster in steel than in air.

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