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Write an equation for the wave as a function of position and time. A wave is modeled with the function y (x, t) = (0.25 m) cos (0.30 m −1 x − 0.90 s −1 t + π 3). Find the (a) amplitude, (b) wave number, (c) angular frequency, (d) wave speed, (e) initial phase shift, (f) wavelength, and (g) period of the wave.
Write down the solution of the wave equation u tt = u xx with ICs u (x; 0) = f (x) and u t (x; 0) = 0 using D'Alembert's formula. Illustrate the nature of the solution by sketching the ux -pro les y = u (x; t) of the string displacement for t = 0 ; 1=2; 1; 3=2. Solution: D'Alembert's formula is 1 Z x+t
wave travel? 2. The speed of a wave is 65 m/sec. If the wavelength of the wave is 0.8 meters, what is the frequency of the wave? 3. A wave has a frequency of 46 Hz and a wavelength of 1.7 meters. What is the speed of this wave? 4. A wave traveling at 230 m/sec has a wavelength of 2.1 meters. What is the frequency of this wave? 5.
A sinusoidal wave travels down a taut, horizontal string with a linear mass density of μ = 0.060 kg/m. The maximum vertical speed of the wave is v y max = 0.30 cm/s. The wave is modeled with the wave equation y (x, t) = A sin (6.00 m −1 x − 24.00 s −1 t).
30 Δεκ 2020 · Combining the dependencies on space and time in a single expression, we can write for the sinusoidal wave: \[u(x, t)=A \cos (k x-\omega t) \label{9.1}\] Figure \(\PageIndex{1}\): Two basic types of waves.
2. Sinusoidal waves We have seen that the wave equation is solved by the d’Alembert solution y(x;t) = f(x ct) + g(x+ ct). A particularly interesting option for f(u) and g(v) are sines and cosines. For example, we can choose f(x ct) = Ccos(k(x ct) + ’): (2.1) The sinusoidal wave is charaterised by Wavenumber = k, Wavelength = 2ˇ=k,
Finding the characteristics of a sinusoidal wave. To find the amplitude, wavelength, period, and frequency of a sinusoidal wave, write down the wave function in the form \(y(x, t)=A \sin (k x-\omega t+\phi)\). The amplitude can be read straight from the equation and is equal to \(A\).
