Question

A 22.1 ºC, 19.48 m long, Silver rod (Y = 72 GPa, ρ = 10.49 g/cm3) is supported at a point (node) between the ends of the rod. Placing a vibrating 269 Hz tuning fork on the support causes a third overtone standing sound wave to develop in the metal.

(a) Calculate the speed of sound in the metal.    m/s

(b) Determine the location of the first and second nodes relative to either end of the rod.

First Node.  m

Second Node.  m

Answer 1

Step 1 of 3

For a Silver rod, we need to find (a) The Speed of sound in the metal. (b) To determine the loccation of the first node amd the second node which is relative to either ends of the rod.

Step 2 of 3

(a)

Given, Young's Elastic modulus of the silver rod =

Density of the silver rod

The speed of sound in the metal is calculated using the equation,

.....(1)

where, is the Young's elastic modulus of the metal and is the density of the metal.

Step 3 of 3

Substituting the values in (1) we get,

Hence, the speed of sound in the metal is,