Calculate the length of an iron rod which can be used to produceultrasonic waves of 20 KHz. Density of iron is 7.23 x103kg/m3andYoung’s modulus is 11.6 x 1010 N/m2

To calculate the length of an iron rod that can produce ultrasonic waves of 20 KHz, we need to use the formula for the speed of sound in a solid rod, which is given by:

v = sqrt(Y/ρ)

where: v is the speed of sound, Y is Young's modulus, and ρ is the density of the material.

Given that the density of iron (ρ) is 7.23 x 10^3 kg/m^3 and Young's modulus (Y) is 11.6 x 10^10 N/m^2, we can substitute these values into the formula to find the speed of sound in iron:

v = sqrt((11.6 x 10^10 N/m^2) / (7.23 x 10^3 kg/m^3)) v = sqrt(1.604 x 10^7 m^2/s^2) v = 4005 m/s

The frequency (f) of the ultrasonic waves is given as 20 KHz, or 20 x 10^3 Hz. The wavelength (λ) of the waves can be found using the formula:

v = fλ

Rearranging for λ gives:

λ = v / f

Substituting the known values gives:

λ = (4005 m/s) / (20 x 10^3 Hz) λ = 0.20025 m

However, for a rod, the length required to produce a wave of a given wavelength is half the wavelength (since the wave must travel to the end of the rod and back), so the length of the rod (L) is:

L = λ / 2 L = 0.20025 m / 2 L = 0.100125 m

So, the length of the iron rod which can be used to produce ultrasonic waves of 20 KHz is approximately 0.100125 meters, or 10.0125 cm.