Mathematics 5 SN SINUSOIDAL GRAPHS AND WORD PROBLEMS

Mathematics 5 SN SINUSOIDAL GRAPHS AND WORD PROBLEMS 1 The tuning fork is a device used to verify the standard pitch of musical instruments. The international standard pitch has been set at a frequency of 440 cycles/second. Write a rule in the form f(t) = A sin Bt that expresses this oscillation where t represents the number of seconds.

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2 Many factors influence the deer population in a given habitat: climate, hunting, predators, etc. The following graph shows the evolution of a population of deer as a function of time.

f(x) Number 800

of deer

500

200

2

6

10 14 18 x

Time (years)

Write the rule that can be used to represent this function.

The rule of this function is __________________________________________________

3 The pendulum of a Grandfather clock completes 20 cycles/minute. It moves a distance of 30 cm. Write a rule in the form f(t) = A sin Bt which expresses the movement of the pendulum where t represents the number of minutes.

30

The rule is ______________________________.

4 An oscillatory movement is expressed by the equation f(t) = 160 sin(500t 100).

Find

a) its frequency b) its period c) its phase shift d) its amplitude

a) _________________________ b) _________________________ c) _________________________ d) _________________________

5 A sound wave is described by a sinusoidal movement whose equation is : f(t) = -230 sin(30t 20).

Find

a) the amplitude b) the period c) the frequency d) the phase shift

a) _________________________ b) _________________________ c) _________________________ d) _________________________

6 Radio station CKOI-FM broadcasts through a frequency of 97 KHz, or 97 000 cycles/s. The radio's volume is set at 5, thus determining the sound amplitude. Write a rule in the form f(t) = A sin Bt of the sinusoidal curve representing the sound waves transmitted.

The rule is ______________________________.

7 For each of the following graphs, find 1) the amplitude 2) the period 3) the frequency 4) the phase shift 5) the equation

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