Given y=2sin2x(100t-x/30) find wave length, frequency and angular frequency?

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.

Wave length (λ):

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)
```

Frequency (f):

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
```

Angular frequency (ω):

The angular frequency is given by:

```
ω = 200π t - πx/30
```

as we found earlier.