A wave, travelling along the x axis, is described by the equationy = 0.14 sin (5.7π t − 0.37π x) where t is in seconds, and x is in metres. Determine thewave’s frequency
Question
A wave, travelling along the x axis, is described by the equationy = 0.14 sin (5.7π t − 0.37π x) where t is in seconds, and x is in metres. Determine thewave’s frequency
Solution
The frequency of a wave is determined by the coefficient of the time variable (t) in the wave equation. In this case, the wave equation is given as y = 0.14 sin (5.7π t − 0.37π x).
The coefficient of t is 5.7π. This value represents the angular frequency of the wave, not the frequency. The angular frequency (ω) and the frequency (f) are related by the equation ω = 2πf.
So, to find the frequency, we can rearrange this equation to solve for f:
f = ω / 2π
Substituting the given angular frequency into this equation gives:
f = 5.7π / 2π
Solving this equation gives the frequency of the wave as f = 5.7 / 2 = 2.85 Hz.
Similar Questions
The sinusoidal wave shown in the figure below is traveling in the positive x-direction and has a frequency of 48.5 Hz.A sinusoidal wave is plotted on a coordinate plane. The wave is vertically centered on the horizontal axis. The vertical distance between a crest and a trough is 8.26 cm, and the horizontal distance between a crest and the nearest trough is 5.20 cm.(a) Find the amplitude. cm(b) Find the wavelength. cm(c) Find the period. s(d) Find the speed of the wave. m/s
A sound wave travels at a speed of 340 m/s. If its wavelength is 1.5 m. What is the frequency of the wave?
A wave has a period of 0.25 seconds. What is the frequency of this wave?
A wave travelling along the x-axis is described by the equation y(x,t) = 0.005cos (αx – βt). If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then α and β in appropriate units are :α = 25.00 π ; β = πα = , β = α = ; β = α = 12.50 π ; β =
The displacement of a wave is given by y = 0.001 sin (100t + x) where x and y are in metre and t is insecond. This represents a wave(a) of wavelength one metre.(b) travelling with a velocity of 100 m/s in the negative x-direction.(c) of frequency (100/π) Hz.(d) travelling with a velocity of 50 π m/s in the positive x-direction
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.