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more than 1 week ago

To find the wavelength, frequency, and angular frequency of the given function y=2sin(2x)(100t-x/30), we need to first identify the parameters of the function.

The general form of a sinusoidal function is y = A sin(Bx + C), where A is the amplitude, B is the angular frequency, and C is the phase shift.

In this case, the function is y = 2sin(2x)(100t-x/30).

Comparing this to the general form, we can see that:

- A = 2 (amplitude)

- B = 2 (angular frequency)

- C = 0 (no phase shift)

The wavelength (λ) of a sinusoidal function is given by the formula λ = 2π/B. In this case, B = 2, so the wavelength is:

λ = 2π/2 = π

The frequency (f) of a sinusoidal function is given by the formula f = B/2π. In this case, B = 2, so the frequency is:

f = 2/2π = 1/π

The angular frequency (ω) of a sinusoidal function is given by the formula ω = 2πf = 2πB. In this case, B = 2, so the angular frequency is:

ω = 2π*2 = 4π

Therefore, the wavelength is π, the frequency is 1/π, and the angular frequency is 4π.

The general form of a sinusoidal function is y = A sin(Bx + C), where A is the amplitude, B is the angular frequency, and C is the phase shift.

In this case, the function is y = 2sin(2x)(100t-x/30).

Comparing this to the general form, we can see that:

- A = 2 (amplitude)

- B = 2 (angular frequency)

- C = 0 (no phase shift)

The wavelength (λ) of a sinusoidal function is given by the formula λ = 2π/B. In this case, B = 2, so the wavelength is:

λ = 2π/2 = π

The frequency (f) of a sinusoidal function is given by the formula f = B/2π. In this case, B = 2, so the frequency is:

f = 2/2π = 1/π

The angular frequency (ω) of a sinusoidal function is given by the formula ω = 2πf = 2πB. In this case, B = 2, so the angular frequency is:

ω = 2π*2 = 4π

Therefore, the wavelength is π, the frequency is 1/π, and the angular frequency is 4π.

Google Gemini AI

more than 1 week ago

The wavelength is given by:

```

λ = 2πv / ω

```

where:

- v is the wave speed

- ω is the angular frequency

From the given equation, we can see that:

```

ω = 200π t - πx/30

```

and

```

v = dx/dt = 100

```

Substituting these values into the equation for wavelength, we get:

```

λ = 2π - 100 / (200π t - πx/30) = 60/(2t - x/30)

```

The frequency is given by:

```

f = ω / 2π

```

Substituting the expression for ω from above, we get:

```

f = (200π t - πx/30) / 2π = 100 - x/60

```

The angular frequency is given by:

```

ω = 200π t - πx/30

```

as we found earlier.