The equation y=5 sin(3x-4), where y is in mm, x is in m and t is in secs, represents a wave motion. Determine the frequency, period and speed of the wave

You mean:

y = 5 sin (3x - 4 t)
without t, no wave

now lets look when t = 0
y = 5 sin 3x
y = 0 when x = 0
but this starts over when
3x = 2 pi
so
when x = (2/3) pi, new period
so
Wavelength = L = 2 pi/3

Now look at x = 0, how long for a period
t = 0 --> 0
4t = 2pi is a new one
so
t = pi/2 is a period

and of course
frequency = 1/period :)

Now if you divide wavelength by period you get speed
speed = distance/time
= [2 pi/3] / [pi/2] = (4/3) meter/sec

To determine the frequency, period, and speed of the wave, we need to understand the equation and its components.

The general equation for a wave motion is y = A sin(Bx - Ct), where A is the amplitude, B is the wave number, and C is the angular frequency.

In our given equation y = 5 sin(3x - 4), we can compare this to the general equation:

Amplitude (A) = 5 (mm)

Comparing the inside of the sine function, we have (3x - 4). From this, we can determine the wave number (B) and the angular frequency (C).

Wave number (B) = 3

Angular Frequency (C) = 1

Now, we can find the frequency, period, and speed of the wave using the following formulas:

Frequency (f) = C / (2π)
Period (T) = 1 / f
Speed (v) = λ × f

In our case, the wave number (B) represents the number of wavelengths per unit distance (in meters). Therefore, wave number B is the reciprocal of the wavelength (λ), so:

Wave number (B) = 2π / λ

Let's solve for λ:

λ = 2π / B
λ = 2π / 3

Now we can calculate the frequency, period, and speed:

Frequency (f) = C / (2π)
f = 1 / (2π / 3)
f = 3 / (2π)

Period (T) = 1 / f
T = 1 / (3 / (2π))
T = (2π) / 3

Speed (v) = λ × f
v = (2π / 3) × (3 / (2π))
v = 1 m/sec

Therefore, the frequency of the wave is 3 / (2π), the period is (2π) / 3, and the speed of the wave is 1 m/sec.

To determine the frequency, period, and speed of the wave represented by the equation y = 5sin(3x - 4), we need to understand the properties of the sine function and how they relate to wave motion.

1. Frequency:
The frequency of a wave represents the number of complete cycles it completes in a given time period. In this case, the equation can be written as y = 5sin(3x - 4(1/3)). Comparing this to the standard form of a sine function, y = A*sin(Bx - C), we can determine that B, which is equal to 3, represents the frequency. Therefore, the frequency of this wave is 3 cycles per meter.

2. Period:
The period of a wave represents the time it takes for one complete cycle to occur. The period can be calculated using the formula T = 1/f, where T is the period and f is the frequency. In this case, the frequency is 3 cycles per meter, so the period can be calculated as T = 1/3. Therefore, the period of this wave is 1/3 meters.

3. Speed:
The speed of a wave represents the distance it travels per unit of time. For wave motion, the speed can be calculated using the formula v = λ * f, where v is the speed, λ (lambda) is the wavelength, and f is the frequency. In this case, the wavelength can be calculated as λ = 1/f, since the frequency is given as cycles per meter. Therefore, the wavelength is λ = 1/3 meters. Using this information, we can calculate the speed of the wave as v = (1/3) * 3 = 1 m/s.

In summary, for the wave represented by the equation y = 5sin(3x - 4), the frequency is 3 cycles per meter, the period is 1/3 meters, and the speed is 1 m/s.

Solve