Question

Determine the speed of sound through an aluminum rod and the wavelength of the sound waves produced by a 440 Hz vibration in the rod. Elastic modulus of aluminium is 70*10^5 N/m^2 Density is 2.7*10^3 Kg/m^3 Options- 1. 300 m/s, 6.2 m 2. 474 m/s , 7.4 m 3. 6340 m/s , 14 m 4. 5090 m/s , 11.6 m

Answer 1

Answer:

option 4 is correct.

Explanation:

Speed of the sound

$v= \sqrt{\frac{E}{\rho} }$

where E=  Elastic modulus of aluminium is 70*10^5 N/m^2

and ρ Density of material=2700 Kg/m^3

therefore, $v =\sqrt{\frac{70\times10^5}{2700} }$

=50.91 m/s.

Now. wavelength $\lambda =\frac{v}{\nu}$

\nu =440 Hz or s^-1, v= 50.91 m/s

therefore, $\lambda =\frac{50.91}{440}$

=0.1157 m.

Answer 2

Given : the sound waves produced by a 440 Hz vibration in the rod. Elastic modulus of aluminium is 70 × 10^9 N/m² Density is 2.7 × 10³ Kg/m³

To find : the speed of sound through the aluminium rod and the wavelength of the sound waves produced.

solution : speed of sound wave, $v=\sqrt{\frac{\gamma}{\rho}}$

where γ is elastic modulus of aluminium rod and ρ is density of the rod.

here γ = 70 × 10^9 N/m², ρ = 2.7 × 10³ kg/m³

so v = √{70 × 10^9/2.7 × 10³}

= √{70 × 10⁶/2.7} ≈ 5090 m/s

Therefore the speed of sound is 5090 m/s in the aluminium rod.

wavelength = speed of sound/frequency

= 5090/440 ≈ 11.6 m

Therefore the wavelength of the sound waves produced by vibration in the rod is 11.6 m

option (4) is correct choice.