A plane wave has an equation y=25 sin(120t - 4x), find wavelength in meters,frequency,period,velocity and amplitude.

when 120 t = 2 pi that t is a period T

when 4 x = 2 pi, that x is a wavelength L
f = 1/T
v = L/T
amplitude is given 25

Can u pls help with this problem

To find the wavelength, frequency, period, velocity, and amplitude of a plane wave with the equation y = 25 sin(120t - 4x), we can analyze the equation and use the appropriate formulas.

1. Wavelength:
The wavelength (λ) of a wave is the distance between two consecutive points in the same phase. In this case, the equation is in the form y = 25 sin(k(x-vt)), where k is the wave number and k = 2π/λ. By comparing the equation to the standard form, we can find the wave number:

k = 4
k = 2π/λ

Rearranging the equation, we can solve for λ (wavelength):

λ = 2π/k
λ = 2π/4
λ = π/2

Therefore, the wavelength of the wave is π/2 meters.

2. Frequency:
The frequency (f) of a wave is defined as the number of complete cycles per unit of time. It is measured in hertz (Hz). We can find the frequency using the formula:

v = fλ

Given that the wave velocity (v) is 120 m/s and the wavelength (λ) is π/2 meters (from the previous step), we can rearrange the formula to solve for frequency:

f = v/λ
f = 120 / (π/2)
f = 240/π

Therefore, the frequency of the wave is 240/π Hz.

3. Period:
The period (T) of a wave is the time it takes for one complete cycle. It is the inverse of the frequency and can be calculated as:

T = 1/f
T = 1 / (240/π)
T = π/240

Therefore, the period of the wave is π/240 seconds.

4. Velocity:
The velocity (v) of a wave is the speed at which the wave propagates through a medium. In this case, the velocity is given as 120 m/s.

Therefore, the velocity of the wave is 120 m/s.

5. Amplitude:
The amplitude (A) of a wave is the maximum displacement from the equilibrium position. In this case, the amplitude is given as 25.

Therefore, the amplitude of the wave is 25.

To summarize:
- Wavelength: π/2 meters
- Frequency: 240/π Hz
- Period: π/240 seconds
- Velocity: 120 m/s
- Amplitude: 25 meters

To find the wavelength, frequency, period, velocity, and amplitude of the given plane wave with the equation y = 25 sin(120t - 4x), we can use the general equation for a plane wave:

y = A * sin(kx - ωt)

where:
y represents the displacement of the wave,
A represents the amplitude of the wave,
k represents the wave number or 2π divided by the wavelength,
x represents the spatial coordinate,
ω represents the angular frequency or 2π times the frequency, and
t represents the time.

Now, let's compare the given equation with the general equation to find the values we need:

1. Amplitude (A):
In our equation, the coefficient of sin(120t - 4x) is 25, which corresponds to the amplitude of the wave. Therefore, the amplitude is A = 25.

2. Wave number (k) and Wavelength (λ):
Comparing the given equation with the general equation, we can determine the value of k. In our equation, k is the coefficient of 'x', so k = 4.
To find the wavelength (λ), we use the formula λ = 2π/k. Plugging in the value of k, we have:
λ = 2π/4 = π/2 ≈ 1.57 meters (rounded to two decimal places).

3. Angular Frequency (ω), Frequency (f), and Period (T):
From the given equation, ω is the coefficient of 't', so ω = 120.
To find the frequency (f), we use the formula f = ω/2π. Plugging in the value of ω, we have:
f = 120/2π ≈ 19.1 Hz (rounded to one decimal place).
To find the period (T), we use the formula T = 1/f. Plugging in the value of f, we have:
T = 1/19.1 ≈ 0.052 seconds (rounded to three decimal places).

4. Velocity (v):
The velocity of the wave can be calculated using the formula v = λf, where λ is the wavelength and f is the frequency. Plugging in the values we found earlier:
v = (π/2) * 19.1 ≈ 29.97 meters per second (rounded to two decimal places).

In summary:
- Wavelength (λ) = 1.57 meters
- Frequency (f) ≈ 19.1 Hz
- Period (T) ≈ 0.052 seconds
- Velocity (v) ≈ 29.97 meters per second
- Amplitude (A) = 25