Also, I need the answer in like 5 mins. This is kinda hard for me can someone help me. It's about the solar system.

North star, its close to our solar system but not in it. hope this helps

Given Information:  

Speed = v = 40 cm/s = 0.40 m/s

Linear density of the string = μ = 4.0 g/cm = 0.4 kg/m

Required Information:  

(a) the frequency = ?

(b) the wavelength of the wave = ?

(c) y_m = ?

(d) k = ?

(e) ω = ?

(f) the correct choice of sign in front of ω = ?

(g) What is the tension in the string = ?

(a) the frequency = 2/π Hz

(b) the wavelength of the wave = 0.628 m

(c) y_m = 0.05 m

(d) k = 10 m⁻¹

(e) ω = 4.0 s⁻¹

(f) the correct choice of sign in front of ω = negative sign

(g) What is the tension in the string = 0.064 N.

Explanation:

The standard form of the equation is given as

y(x, t) = y_m sin(kx ± ωt)

Whereas the given equation is

y=(5.0cm)sin[1.0−(4.0s⁻¹)t]

(a) the frequency

comparing the given equation with the standard form yields,

ωt = (4.0s⁻¹)t

ω = 4.0 s⁻¹

We also know that

ω = 2πf

4.0 = 2πf

f = 4.0/2π

f = 2/π Hz

Therefore, frequency of the wave is 2/π Hz

(b) the wavelength of the wave

We know that wavelength is given by

λ = v/f

Where λ is the wavelength, v is the speed of wave and f is the frequency of sinusoidal wave.

λ = 0.40/(2/π)

λ = 0.20π

λ = 0.628 m

(c) y_m

comparing the given equation with the standard form yields,

y_m = 5 cm

or

y_m = 0.05 m

This is the amplitude of the sinusoidal wave

(d) k

comparing the given equation with the standard form yields,

kx = 1

k = 1/x

k = 1/0.10

k = 10 m⁻¹

(e) ω

already calculated in part (a)

ω = 4.0 s⁻¹

(f) the correct choice of sign in front of ω?

comparing the given equation with the standard form, a negative sign is the correct choice of sign in front of ω.

(g) What is the tension in the string?

We know that tension in the string is given by

T = μv²

Where μ is the linear density of the string and v is the speed of the wave.

T = 0.4(0.40)²

T = 0.064 N

Therefore, the tension in the string is 0.064 N.