2018 A/L Physics Past Paper · Question 04 (English Medium)

Answer: (2) only C is true.

What the question asks

We want: which of the statements A, B and C about the speed of sound $v$ in an ideal gas are true?

We test each statement on its own.

Relevant theory

(2) dependent on temperature with the velocity increasing with increasing temperature.

(1) independent of pressure

The speed of sound in an ideal gas is

$$v = \sqrt{\frac{\gamma R T}{M}}$$

$T$ is the absolute temperature.

$M$ is the molar mass.

$\gamma$ is the ratio of the molar heat capacities, $C_p / C_v$.

Reading the options

Each option is a group of statements.

First we judge A, B and C. Then we pick the group that matches.

Reasoning and calculation

$v \propto T$

$T$ is under the square root.

So $v$ goes with $\sqrt{T}$, not with $T$.

Make $T$ four times bigger. Then $v$ is only two times bigger.

So A is false.

A

$v \propto 1/M$

$M$ is under the square root too.

So $v$ goes with $1/\sqrt{M}$, not with $1/M$.

Make $M$ four times bigger. Then $v$ becomes half, not a quarter.

So B is false.

B

v depends on γ

$\gamma$ is in the formula.

So a different $\gamma$ gives a different $v$.

For example, at the same $T$ and $M$, a gas with $\gamma = 1.67$ and a gas with $\gamma = 1.4$ have different speeds.

So C is true.

C

A and B make the same mistake.

They forget the square root.

The right way: $v \propto \sqrt{T}$ and $v \propto 1/\sqrt{M}$.

Why the other options fail

This option says: only A is true.

But A is false.

And C is true, but it leaves C out.

So it is wrong.

This option says: only A and B are true.

But A and B are both false.

This option says: only B and C are true.

C is true. But B is false.

This option says: all A, B and C are true.

But A and B are false.

Conclusion

$v = \sqrt{\frac{\gamma R T}{M}}$

A is false. B is false. C is true.

$$v = \sqrt{\frac{\gamma R T}{M}}$$

The answer is option (2): only C is true.

v ∝ T, v ∝ 1/M

Remember the square root: $v \propto \sqrt{T}$ and $v \propto 1/\sqrt{M}$.