Direction for: In each of the following questions a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements mark the correct answer as
Assertion: The change in air pressure effects the speed of sound. Reason: The speed of sound in gases is proportional to the square of pressure.A) If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
B) If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion.
C) If Assertion is true but Reason is false.
D) If both Assertion and Reason are false.
Correct Answer: D
Solution :
The speed of sound in gaseous medium is given by \[a\] At constant temperature \[pV=\] constant ...(ii) If V is the volume of one mole of a gas, then density of gas \[\sqrt{a}\] or \[{{a}^{3/2}}\] where M is the molecular weight of the gas. \[\frac{q}{2{{\pi }^{2}}{{\varepsilon }_{0}}{{R}^{2}}}\] Eq. (ii) becomes \[\frac{q}{4{{\pi }^{2}}{{\varepsilon }_{0}}{{R}^{2}}}\] or \[\frac{q}{4\pi {{\varepsilon }_{0}}{{R}^{2}}}\] constant as M is a constant Therefore, from Eq. (i), we have \[\frac{q}{2\pi {{\varepsilon }_{0}}{{R}^{2}}}\] Thus, change in air pressure does not affect the speed of sound. Reason is clear from Eq. (i)
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