# Sine functions and Sound Waves - An Investigation

- Author:
- yogaaum8, Andy Collins, mathe-wiki.com

Note this page is divided into various activities which you must engage with and complete.
Task 1: Sine function applet with sliders to explore the effect of changing the variable on the function.
Task 2A: Recording the effects of the variable on the given sine function.
Task 2B: Answering questions on the "Properties of a sine function".
Task 3: Applet to explore the effect of amplitude and frequency of a sine function on a sound wave.
Task 4: Answering questions on "Properties of sound waves in terms of their respective sine functions".
Below is the first of the tasks.
Task 1: Sine function applet with sliders to explore the effect of changing the variable on the function.
Use the sliders to help you explore the effect of changing each of the variables for the given sine function. Record the effect of the change of each variable on the sine function and its graph in the space provided below.
Use your findings to answer the questions below labelled "Record of findings". You may return to the graph to assist you in answering each question.

## Task 2A: Record of findings of the effect of each variable on the given sine function. 4 marks

## Task 2B: Properties of a sine function

Questions:
1) Place the appropriate letter (a,b,h or k) in the equation where it belongs
f(x) = ___ sin ___( x - ___) + ___ 1 mark
2) Define what changing the a value does to the graph 1 mark
3) Define what changing the b value does to the graph 1 mark
4) Define what changing the h value does to the graph 1 mark
5) Define what changing the k value does to the graph 1 mark
6) Below are terms used for each of those 4 values - please write to corresponding letter for each term: 4 Marks
Phase Shift ___
Vertical Shift___
Frequency ___
Amplitude ___
7) With the values of a=1, b=1, h=0 and k=0 what is the length of one piece of the wave? 1 mark

## Responses for Task 2B: Properties of a sine function

Write your responses to the questions above in this text box

## Use the applet below to explore the effect of amplitude and frequency of sine functions on sound waves.

## Answering questions on "Properties of sound waves in terms of their respective sine functions'.

Use the applet above in task 3 to answer the following questions related to sine functions and their respective sound waves. 1. What part of the sine function relates to the volume of sound? 1 mark 2. What part of the sine function relates to the pitch of sound? 1 mark