Given that young's modulus for aluminium is 7.0 x 1010Nm-2 and density is 2.7 x 103kgm-3 find the speed of the sound produced if a solid bar is struck at one end with a hammer
A. 5.1 x 103ms-1
B. 4.2 x 103ms-1
C. 3.6 x 103ms-1
D. 2.8 x 103ms-1
To find the speed of sound in a solid bar struck with a hammer, we can use the formula:
v = √(Y/ρ)
where v is the speed of sound, Y is the Young's modulus, and ρ is the density.
Plugging in the values:
v = √(7.0 x 10^10 Nm^-2 / 2.7 x 10^3 kgm^-3)
Calculating this:
v ≈ √(2.6 x 10^7)
v ≈ 5.1 x 10^3 ms^-1
Therefore, the correct answer is A. 5.1 x 10^3 ms^-1.
To find the speed of sound produced in the solid bar, we can use the formula for the speed of sound in a solid:
v = √(Y / ρ)
Where:
- v is the speed of sound
- Y is the Young's modulus
- ρ is the density
Let's plug the given values into the formula:
v = √(7.0 x 10^10 N/m^2 / 2.7 x 10^3 kg/m^3)
v = √(7.0 x 10^10 / 2.7 x 10^3) m/s
Simplifying,
v = √(25.9259259259 x 10^6) m/s
v ≈ √(26 x 10^6) m/s
v ≈ 5.1 x 10^3 m/s
Therefore, the speed of sound produced in the solid bar when struck at one end is approximately 5.1 x 10^3 m/s.
The answer is A. 5.1 x 10^3 m/s.