Question

A 90.0-m-long brass rod is struck at one end. A person at the other end hears two sounds as a result of two longitudinal waves, one traveling in the metal rod and the other traveling in the air. What is the time interval between the two sounds? Take the speed of sound in air to be 344 m/s. Use 8600 kg/m3 for the density of brass and 9.00×109 Pa for Young's modulus of brass.

Answer 1

Answer:

0.174413400763 s

Explanation:

L = Length of rod = 90 m

Speed of sound in air = 344 m/s

$\rho$ = Density of brass = 8600 kg/m³

Y = Young's modulus = $9\times 10^9\ Pa$

Velocity of sound in a material is given by

$v_b=\sqrt{\dfrac{Y}{\rho}}\\\Rightarrow v_b=\sqrt{\dfrac{9\times 10^9}{8600}}\\\Rightarrow v_b=1022.99150921\ m/s$

Time taken in brass

$t=\dfrac{L}{v_b}\\\Rightarrow t=\dfrac{90}{1022.99150921}\\\Rightarrow t=0.0879772697913\ s$

In air

$t=\dfrac{L}{v}\\\Rightarrow t=\dfrac{90}{343}\\\Rightarrow t=0.262390670554\ s$

The time interval is $0.262390670554-0.0879772697913=0.174413400763\ s$