Question

for aluminium bluk modalous is 7.5×10^10 Nm^2 and density is 2.70×10^3kgm^3 find the velosityof longitudnal waves in alminium​

Answer 1

$\huge{\green{\underline{\underline{Answer:-}}}}$

Given:

Bulk modulus = 7.5 × 10^10 Nm²

Density = 2.7 × 10³ kg m³

To find:

Velocity of longitudinal waves in aluminium = ?

Explanation:

The velocity of longitudinal waves in aluminium is given as

$\\ \\ v = \sqrt{ \dfrac{k}{ρ} } \\ \\ k \: or \: B \: \: is \: bulk \: modulus \\ \\ d \: \: or \: \: ρ \: \: is \: \: density$

$\\ \\ v = \sqrt{ \dfrac{7.5 \times 10 {}^{10} }{2.7 \times 10 {}^{3} } } \\ \\ v = \sqrt{ \dfrac{7.5 \times 10 {}^{7} }{2.7} } \\ \\ v = \sqrt{2.77 \times 10 {}^{7} }$

$\\ \\ v = \sqrt{27.7 \times 10 {}^{6} } \\ \\ v = 5.26 \times 10 {}^{3} \\ \\ v ≈5.3 \times 10 {}^{3} m /sec$

Answer:

Thus, velocity of longitudinal waves in aluminium is 5.3 × 10³ m/ sec

Knowledge booster:

1. Bulk modulus is the modulus of elasticity related to change in volume of body due to applied deforming force
2. In the formula v = √k/d, k or bulk modulus can be replaced by young modulus as per question
3. Try to solve more such questions to get good hold on it