2019 A/L Physics Past Paper · Question 11 (English Medium)

Answer: (4) Only A and C

What the question asks

We want:

Which of the three statements about the speed of sound in the air are correct.

A: it does not change with height at constant temperature.

B: it always rises when the pressure falls.

C: it falls with height because the temperature falls.

Relevant theory

is another expression for the velocity of sound in a gas.

(1) independent of pressure

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

The speed of sound in a gas:

$$v = \sqrt{\dfrac{\gamma RT}{M}}$$

For air, $\gamma$ and $M$ do not change.

So $v$ depends only on the temperature $T$. $v \propto \sqrt{T}$.

It can also be written $v = \sqrt{\dfrac{\gamma p}{\rho}}$.

At constant $T$, $p$ and $\rho$ change in the same ratio. So $\dfrac{p}{\rho}$ stays the same.

Reading the options

The options list the statements that are correct.

Judge A, B and C first. Then pick the matching option.

Reasoning and calculation

Does not change with altitude at constant temperature

At constant temperature $v = \sqrt{\dfrac{\gamma RT}{M}}$ does not change.

The pressure falls with height. But the density falls in the same ratio.

So $v$ does not change.

So A is correct.

A

Always increases as the pressure falls

The speed of sound does not depend on the pressure.

At constant $T$ it does not change. If $T$ falls, it falls.

So B is wrong.

B

Decreases with height because the temperature falls

In the lower air the temperature falls as we go up.

$v \propto \sqrt{T}$. So $v$ falls too.

So C is correct.

C

Only B is wrong.

It treats the pressure as the cause. Only the temperature changes $v$.

A and C both follow from the same rule.

$340$

$v = 331 \sqrt{\frac{288}{273}}$

$295$

$v = 331 \sqrt{\frac{217}{273}}$

Why the other options fail

C is missing.

B is a wrong statement.

A is missing.

It includes B as well.

Conclusion

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

The speed of sound depends only on the temperature.

A and C are correct. B is wrong.

So the answer is option (4).

Thinking that sound goes faster up high because the air is thinner.

Pressure and density fall together. Their effects cancel. The colder temperature lowers the speed.