A wave produced by a simple harmonic oscillator whose displacement in meters is given by the equation: y = 0.3 sin (3πx + 24πt), what is the frequency? [1] 3 Hz   [2] 7.2 Hz   [3] 8...

A wave produced by a simple harmonic oscillator whose displacement in meters is given by the equation: y = 0.3 sin (3πx + 24πt),

what is the frequency?

[1] 3 Hz  

[2] 7.2 Hz  

[3] 8 Hz  

[4] 12 Hz  

[5] 24 Hz

Asked on by saj-94

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to use the following equation that helps you to evaluate the frequency, under the given conditions, such that:

`f = 1/T`

`T` represents the period of wave motion

Since the frequency depends on the period of motion, you need to evaluate the period, hence, you need to use the following formula, such that:

`T = (2pi)/(omega)`

You need to identify the angular velocity `omega` , which is the coefficient of time t, hence, `omega = 24pi` .

`T = (2pi)/(24pi)`

Reducing duplicate factors yields:

`T = 1/12`

You may evaluate the frequency replacing `1/12` for `T` in equation of frequency, such that:

`f = 1/(1/12) => f = 12 Hz`

Hence, evaluating the frequency, under the given conditions, yields `f = 12 Hz` , hence, you need to select the answer `[4] 12 Hz.`

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