Verified Solution • 2025–26 Session moderate

Q14.4: NCERT Physics - Part 2 WAVES 14.4 Solution: Use the formula to explain why the speed of sound in air (a) is …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat $P$ and $\rho$ as independent in $v=\sqrt{\gamma P/\rho}$ and conclude that higher pressure raises sound speed; remember that for an ideal gas $P=\rho R T/M$, so at constant $T$ the ratio $P/\rho$ is fixed. Likewise, humidity changes the mean molecular weight (and thus $\rho$) while total pressure stays nearly constant, so the speed increase comes from reduced density, not a direct pressure effect.

Use the formula

v = \sqrt{\frac{\gamma P}{\rho}}

to explain why the speed of sound in air (a) is independent of pressure, (b) increases with temperature, (c) increases with humidity.

Step-by-Step Verified Solution

**Answer:** (a)

P/\rho

is constant at constant T. (b)

v \propto \sqrt{T}

. (c) Humidity decreases density. **Step-by-Step Explanation:** (a) For an ideal gas,

P/\rho = RT/M

. At constant temperature,

P/\rho

is constant, so

v

is independent of pressure . (b) Since

P/\rho \propto T

, we have

v \propto \sqrt{T}

. Hence

v

increases with temperature . (c) The density of water vapour is less than that of dry air. Adding humidity decreases the average density

\rho

, so

v

increases [citation:3].

All Questions in this Chapter

Q14.1 Q14.2 Q14.3 Q14.4 Q14.5 Q14.6 Q14.7 Q14.8 Q14.9 Q14.10 Q14.11 Q14.12 Q14.13 Q14.14 Q14.15 Q14.16 Q14.17 Q14.18 Q14.19

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