If the Young's modulus of the material of a rod is 2 × 1011 N m -2 and its density is 8000 kg m -3, the time taken by a sound wave to traverse 1 m of the rod will be

Question

If the Young's modulus of the material of a rod is 2 × 1011 N m -2 and its density is 8000 kg m -3, the time taken by a sound wave to traverse 1 m of the rod will be (A) 3 × 10-4 s (B) 2 × 10-4 s (C) 3 × 10-2 s (D) 2 × 10-2 s

Tardigrade Admin · Accepted Answer

The speed of sound waves in the rod is v=√(Y/ρ)=√(2 × 1011/8000)=5000 m s -1 ∴ Time taken =(1/5000)=2 × 10-4 s

Q. If the Young's modulus of the material of a rod is $2 \times 1 0^{11} N m^{- 2}$ and its density is $8000 k g m^{- 3}$ , the time taken by a sound wave to traverse $1 m$ of the rod will be

$3 \times 1 0^{- 4} s$

$2 \times 1 0^{- 4} s$

$3 \times 1 0^{- 2} s$

$2 \times 1 0^{- 2} s$

The speed of sound waves in the rod is
$v = \frac{Y}{ρ} = \frac{2 \times 1 0 ^{11}}{8000} = 5000 m s^{- 1}$
$∴$ Time taken $= \frac{1}{5000} = 2 \times 1 0^{- 4} s$

Q. If the Young's modulus of the material of a rod is 2×1011Nm−2 and its density is 8000kgm−3, the time taken by a sound wave to traverse 1m of the rod will be

3×10−4s

2×10−4s

3×10−2s

2×10−2s