0

Guest

Courses New

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

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

Grade:12

1 Answers

Arun
25750 Points
5 years ago
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

Think You Can Provide A Better Answer ?

Other Related Questions on General Physics

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More