Question

A wave traveling in a string in the positive x direction has a wavelength of 35 cm, an amplitude of 8.4 cm, and a period of 1.2 s. what is the wave equation (in base si units) that correctly describes this wave? a wave traveling in a string in the positive x direction has a wavelength of 35 cm, an amplitude of 8.4 cm, and a period of 1.2 s. what is the wave equation (in base si units) that correctly describes this wave? y(x,t)=0.084 sin(18x−5.2t) y(x,t)=0.084 sin(0.35x+1.2t) y(x,t)=0.084 sin(2.9x−0.83t) y(x,t)=0.084 sin(18x+5.2t) y(x,t)=0.084 sin(0.35x−1.2t)

Answer 1

The correct wave equation which describes the wave with given amplitude, wavelength, and period in base SI units is y(x,t) = 0.084 sin(18x−5.2t).

Step-by-step explanation:

The wave traveling in the string in the positive x direction, with a wavelength of 35 cm, an amplitude of 8.4 cm, and a period of 1.2 s, can be described using a sinusoidal wave equation. To convert to base SI units, we must have wavelength λ in meters (m), amplitude A in meters (m), and the period T in seconds (s). Using the wave equation y(x, t) = A sin(kx - ωt + φ), where k is the wave number (2π/λ) and ω is the angular frequency (2π/T), we can calculate the correct constants.

First, we convert the amplitude to meters: 8.4 cm = 0.084 m. Next, we convert the wavelength to meters: 35 cm = 0.35 m. Then, we calculate k = 2π/0.35 m⁻¹, and ω = 2π/1.2 s⁻¹. Inserting these values into the wave equation gives us: y(x, t) = 0.084 sin(2π/0.35 x - 2π/1.2 t), which simplifies to y(x, t) = 0.084 sin(18 x - 5.2 t). Therefore, the correct wave equation in base SI units that describes this wave is y(x,t) = 0.084 sin(18x−5.2t).

Answer 2

The correct answer is
y(x,t)=0.084 sin(18x-5.2t)
Let's see why.

For a wave travelling in the positive x-direction, the wave equation can be written as

`y(x,t) =A \sin (kx-\omega t)`
where
A is the amplitude

`k= (2 \pi)/(\lambda)` is the wave number

`\omega = (2 \pi)/(T)` is the angular frequency

The wave in our problem has an amplitude of

`A=8.4 cm = 0.084 m`
A wave number of (the wavelength is
`\lambda=35 cm = 0.35 m` )

`k= (2 \pi)/(\lambda)= (2 \pi)/(0.35 m)= 18 m^(-1)`
and an angular frequency of (the period is T=1.2 s)

`\omega = (2 \pi)/(T)= (2 \pi)/(1.2 s)=5.2 s^(-1)`

So, if we put this numbers into the equation, we find (in SI units):

`y(x,t)=(0.084) \sin (18 x - 5.2 t)`