The speed 'v' of a longitudinal wave in an ideal gas of pressure
| The speed 'v' of a longitudinal wave in an ideal gas of pressure 'P' and density 'ρ' is equal to __________.
A. √(P/ρ)
B. √(ρ/P)
C. (P/ρ)<sup>2</sup>
D. (ρ/P)<sup>2</sup>
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
CONCEPT:
Speed of a longitudinal wave in an ideal gas:
- In a longitudinal wave, the particles of the medium oscillate forward and backward in the direction of propagation of the wave.
- They cause compressions and rarefactions of small volume elements of the medium.
- Speed of a sound wave in an ideal gas is given by:
\(v = \sqrt {\frac{{P}}{ρ }} \)
where P = Pressure of the gas and ρ = density.
EXPLANATION:
- Speed of a sound wave in an ideal gas is given by:
\(v = \sqrt {\frac{{P}}{ρ }} \)
- Therefore option 1 is correct.