2025HSCShort answer

Q15 (a)

2 marks

Question

A sound wave can be modelled using a function $P(t)=k\sin(at)$ , where $P$ is air pressure in Pascals, $t$ is time in milliseconds (ms) and $k$ and $a$ are constants.

Write the equation for a sound wave $P_1(t)$ that has an amplitude of 2 Pascals and a period of 5 ms.

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Solution

Criteria	Marks
Provides correct equation	2
Finds $k$ , or equivalent merit	1

Sample answer:

\begin{aligned} k&=2\\ \text{Period}&=\frac{2\pi}{a}=5\text{ ms}\quad\text{so}\quad a=\frac{2\pi}{5}\\ P_1(t)&=2\sin\frac{2\pi}{5}t \end{aligned}

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Syllabus alignment

Trigonometric Functions

Trigonometric Functions and IdentitiesApply the 2017 Mathematics Advanced syllabus content for trigonometric functions and identities.

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