A sinusoidal wave traveling in the +𝑥 direction (to the right) has an amplitude of 15.0 cm, a wavelength of 10.0 cm and a frequency of 20.0 Hz. At t = 0, a particle at x = 0 has a displacement of 15.0 cm.(a) Write an expression for the wave function, y(x, t).20:39
Question
A sinusoidal wave traveling in the +𝑥 direction (to the right) has an amplitude of 15.0 cm, a wavelength of 10.0 cm and a frequency of 20.0 Hz. At t = 0, a particle at x = 0 has a displacement of 15.0 cm.(a) Write an expression for the wave function, y(x, t).20:39
Solution
The wave function for a sinusoidal wave traveling in the +x direction is given by the equation:
y(x, t) = A sin(kx - wt + φ)
where:
- A is the amplitude of the wave,
- k is the wave number, which is equal to 2π/λ (λ is the wavelength),
- w is the angular frequency, which is equal to 2πf (f is the frequency),
- φ is the phase constant.
Given that the amplitude A = 15.0 cm, the wavelength λ = 10.0 cm, and the frequency f = 20.0 Hz, we can calculate k and w as follows:
k = 2π/λ = 2π/10.0 cm = 0.2π cm^-1 w = 2πf = 2π*20.0 Hz = 40π rad/s
At t = 0, a particle at x = 0 has a displacement of 15.0 cm, which is the maximum displacement. This means that the phase constant φ = 0.
Therefore, the wave function is:
y(x, t) = 15.0 cm sin(0.2πx - 40πt)
Similar Questions
A sinusoidal wave traveling in the +𝑥 direction (to the right) has an amplitude of 15.0 cm, a wavelength of 10.0 cm and a frequency of 20.0 Hz. At t = 0, a particle at x = 0 has a displacement of 15.0 cm.(a) Write an expression for the wave function, y(x, t).20:39b) Determine the speed and acceleration at t = 0.500 s for the particle on the wave located at x = 5.0 cm.20:40
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
A wave is represented by :y (x, t) = (5 cm) sin 1(20 s ) t− 1(15 cm ) x− + Determine the velocity of the wave.
The figure shows how the displacement of particles in a wave varies with distance from the source. Using the figure, determine the amplitude and the wavelength of the wave respectively.*1 point4 mm, 16 mm4 cm, 16 cm4 mm, 16 cm4 cm, 20 cm
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
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.