How much time will elaspe for the microphone picks up a disturbance?

[ohheytai]

One mole of iron (6.02x10^23 atoms) has a mass of 56 grams, and its density is 7.87 grams per cubic centimeter. You have a long thin bar of iron, 2.4 m long, with a square cross section, 0.15 cm on a side.

You hang the rod vertically and attach a 234 kg mass to the bottom, and you observe that the bar becomes 1.22 cm longer. Calculate the effective stiffness of the interatomic bond, modeled as a "spring": answer is 46.5N/m

Next you remove the 234 kg mass, place the rod horizontally, and strike one end with a hammer. How much time t will elapse before a microphone at the other end of the bar will detect a disturbance? i can't find this part i don't know how to do it its no where in my book

 

[anathema]

To calculate the time it takes for a disturbance to travel through the iron bar, we can use the formula for wave speed, v=√(E/ρ), where E is the Young's modulus of iron and ρ is its density.

First, we need to calculate the Young's modulus of iron. This can be done using the formula E = stress/strain, where stress is the force applied and strain is the resulting deformation. In this case, we know that the bar became 1.22 cm longer when a 234 kg mass was attached to the bottom, so the strain is 1.22 cm/2.4 m = 0.0005083. The stress can be calculated using the formula stress = force/area. The area of the cross section of the bar is (0.15 cm)^2 = 0.0225 cm^2. Therefore, the stress is (234 kg)(9.8 m/s^2)/(0.0225 cm^2) = 1.02x10^7 N/cm^2.

Now, we can plug these values into the formula for Young's modulus: E = (1.02x10^7 N/cm^2)/(0.0005083) = 2.01x10^10 N/cm^2.

Next, we can plug this value of E and the density of iron (7.87 g/cm^3) into the formula for wave speed: v= √(2.01x10^10 N/cm^2)/(7.87 g/cm^3) = 5.45x10^3 cm/s.

Finally, we can use the formula for wave speed to calculate the time it takes for a disturbance to travel through the 2.4 m long bar: t = distance/speed = (2.4 m)/(5.45x10^3 cm/s) = 4.40x10^-4 s. Therefore, it would take approximately 0.00044 seconds for a disturbance to travel through the iron bar and reach the microphone at the other end.