# Find the amplitude of a sinusoid given frequency and time after zero-crossing

• jnuz73hbn
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Homework Statement
What is the elongation of a sine wave if the amplitude is 12cm and the frequency is 12Hz after 0.04 s after the zero crossing
Relevant Equations
s=smaxsin (2π f t)
2π f t = 6,28  12  0,04 = 3,0144

Welcome to PF.

berkeman said:
Welcome to PF.

thanks I have it now :)

berkeman

## What is a sinusoid?

A sinusoid is a mathematical curve that describes a smooth, periodic oscillation. It is commonly represented by the sine or cosine functions and is used to model wave-like phenomena, such as sound waves, light waves, and alternating current in electrical circuits.

## How do you define amplitude in a sinusoid?

Amplitude is the maximum displacement of points on a wave, measured from its equilibrium position. In a sinusoidal function, it represents the peak value of the wave. Mathematically, for a sinusoid of the form $$y(t) = A \sin(\omega t + \phi)$$, the amplitude is the constant $$A$$.

## What is the relationship between frequency and amplitude in a sinusoid?

Frequency and amplitude are independent properties of a sinusoid. Frequency measures how many cycles of the wave occur per unit of time, while amplitude measures the height of the wave. Changing the frequency does not affect the amplitude, and vice versa.

## How can you find the amplitude of a sinusoid if you know the frequency and time after zero-crossing?

The amplitude of a sinusoid cannot be directly determined from the frequency and time after zero-crossing alone. The amplitude is a separate parameter that must be given or measured independently. The frequency and time after zero-crossing can help determine the phase and period of the sinusoid but not its amplitude.

## What additional information is needed to determine the amplitude of a sinusoid?

To determine the amplitude of a sinusoid, you need to know the peak value or the maximum displacement of the wave. This can be obtained through direct measurement or provided as part of the sinusoidal function's parameters. Without this information, the amplitude cannot be calculated from frequency and time after zero-crossing alone.

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