Given the following displacement – time graph for a mass oscillating on a spring. i. period ii. Find the frequency of the above wave 14. Two girls stood 200m from a wall. One of the girls banged two p

A complete oscillation is the time taken for the wave to repeat its pattern. From the graph, the wave starts at zero displacement, goes up, down, and returns to zero displacement, moving in the same direction, at $2.0\text{ s}$.
Alternatively, it reaches a peak at $1.0\text{ s}$ and the next peak is at $3.0\text{ s}$. The time between two consecutive peaks is the period.
Period $T = 2.0\text{ s}$.
The period is $\boxed{\text{2.0 s}}$.

Where $f$ is frequency and $T$ is period.

The frequency of the wave is $\boxed{\text{0.5 Hz}}$.

14. Two girls stood $200\text{m}$ from a wall. One of the girls banged two pieces of wood together while the second started a stop watch and stopped it when she heard the echo. If the time shown on the stop watch was $1.2\text{ sec}$ determine the speed of the sound.

The sound travels from the girls to the wall and then reflects back to the girls (echo).
Distance to wall = $200\text{ m}$
Total distance traveled by sound, $d = 2 \times 200\text{ m} = 400\text{ m}$

Given time, $t = 1.2\text{ s}$

The speed of the sound is $\boxed{\text{333.33 m/s}}$.

15. A lawn sprinkler has 40 holes each of cross section area $2.0 \times 10^{-2}\text{ cm}^2$. The sprinkler is connected to a hose pipe of cross section area $1.6\text{ cm}^2$, if the speed of the water in the hose pipe is $1.2\text{ m/sec}$, calculate the flow rate in the hose pipe

Cross-section area of hose pipe, $A_{\text{hose}} = 1.6\text{ cm}^2$
Speed of water in hose pipe, $v_{\text{hose}} = 1.2\text{ m/s}$

The flow rate in the hose pipe is $\boxed{\text{1.92} \times 10^{-4}\text{ m}^3\text{/s}}$.
(Note: The information about the sprinkler holes is not needed to calculate the flow rate in the hose pipe.)

16. State two factors affecting boiling point of a liquid

• External pressure: A higher external pressure increases the boiling point, while a lower external pressure decreases it.
• Impurities: The presence of dissolved impurities (solutes) in a liquid generally increases its boiling point.