A guitar string of length L = 1.01 m is oriented along the x-direction and under a tension of T = 79 N. The string is made of steel which has a density of ρ = 7800 kg / m3. The radius of the string is r = 4.7 x 10-4 m. A transverse wave of amplitude A = 0.0020 m is formed on the string. 1. Assume a form y2 = A sin(α) for the transverse displacement of the string. Write an expression for α of a transverse wave on a string traveling along the negative x-direction in terms of its wavenumber k, the position x, its angular frequency ω, and the time t. 2. Write an equation for a standing wave on the string y(x,t) created by y1(x,t) and y2(x,t) in terms of the amplitude of the original traveling waves A, its wavenumber k, the position x, its angular frequency ω, and the time t. Use a trigonometric identity so that y(x,t) contains a sine term dependent only on k and x and a cosine term dependent only on ω and t.
A guitar string of length L = 1.01 m is oriented along the x-direction and under a tension of T = 79 N. The string is made of steel which has a density of ρ = 7800 kg / m3. The radius of the string is r = 4.7 x 10-4 m. A transverse wave of amplitude A = 0.0020 m is formed on the string.
1. Assume a form y2 = A sin(α) for the transverse displacement of the string. Write an expression for α of a transverse wave on a string traveling along the negative x-direction in terms of its wavenumber k, the position x, its angular frequency ω, and the time t.
2. Write an equation for a standing wave on the string y(x,t) created by y1(x,t) and y2(x,t) in terms of the amplitude of the original traveling waves A, its wavenumber k, the position x, its angular frequency ω, and the time t. Use a trigonometric identity so that y(x,t) contains a sine term dependent only on k and x and a cosine term dependent only on ω and t.
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