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Grade: 12
        
An aluminium rod having a length 100 cm is clamped at its middle point and set into longitudinal vibrations.Let the rod vibrate in its fundamental mode. The density of aluminium is 2600 kg/m3 and its Young’s modulus is 7.8 × 1010 N/m2. The frequency of the sound produced is
one year ago

Answers : (1)

Arun
23011 Points
							
The speed of sound in aluminium will be

v = Y ρ = 7 . 8 × 10 10 2600 = 5480   m / s

Since the rod is clamped at the middle, the middle point is a pressure antinode. The free ends of the rods are the nodes. As the rod vibrates in its fundamental mode, there are no other nodes and antinodes. The length of the rod, which also the distance between the successive nodes, is, therefore, equal to half the wavelength. So, the wavelength of sound in the aluminium rod is 

l = 2 l = 200   c m   =   2   m

Thus, the frequency of the sound produced which is also equal to the frequency of vibration of the rod is 

n = v λ = 5480 2 = 2740   H z
one year ago
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