Answer
Given,
y(x, t) = (3.5 cm) cos(2.7 x − 92 t)
comparing the given equation with general equation
y(x,t) = A cos(k x - ω t)
A = 3.5 cm , k = 2.7 rad/m , ω = 92 rad/s
we know,
a) ω =2πf
f = 92/ 2π
f = 14.64 Hz
b) Wavelength of the wave
we now, k = 2π/λ
2π/λ = 2.7
λ = 2 π/2.7
λ = 2.33 m
c) Speed of wave
v = ν λ
v = 14.64 x 2.33
v = 34.11 m/s
The wavelength of the wave is 0.4299m
The frequency of the wave is 14.65Hz
The speed of the wave is 6.298m/s
The standard equation of a wave is expressed according to the formula;
[tex]y(x,t)=Acos(\frac{2 \pi x}{\lambda} \pm 2\pi ft )[/tex]
f is the frequency of the wave
λ is the wavelength
Given the equation of the wave [tex]y(x,t)=3.5cos(2.7x-92t)[/tex]
Comparing both equations:
[tex]\frac{2 \pi}{\lambda} =2.7\\\lambda = \frac{2.7}{2\pi}\\\lambda = 0.4299m[/tex]
Hence the wavelength of the wave is 0.4299m
Get the frequency of the wave:
[tex]2\pi f = 92\\f=\frac{92}{2\pi} \\f =\frac{92}{6.28}\\f= 14.65 Hz[/tex]
Hence the frequency of the wave is 14.65Hz
Find the speed of the wave:
Speed = frequency * wavelength
Speed = 14.65 * 0.4299
Speed = 6.298m/s
Hence the speed of the wave is 6.298m/s
Learn more on wave equation here: https://brainly.com/question/21013228
