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Consider a uniform string of length 1, tension T, and mass per unit length p that...
A string of length L, mass per unit length mu, and tension T is vibrating at...
A string of length L, mass per unit length mu, and tension T is vibrating at its fundamental frequency. What effect will the following have on the fundamental frequency? The length of the string is doubled, with all other factors held constant. The mass per unit length is doubled, with all other factors held constant. The tension is doubled, with all other factors held constant.
A stretched string has a mass per unit length of 4.82 g/cm and a tension of...
A stretched string has a mass per unit length of 4.82 g/cm and a tension of 12.9 N. A sinusoidal wave on this string has an amplitude of 0.150 mm and a frequency of 168 Hz and is traveling in the negative direction of an x axis. If the wave equation is of the form y(x,t) = ym sin(kx + ωt), what are (a) ym, (b) k, and (c) ω, and (d) the correct choice of sign in front of...
A stretched string has a mass per unit length of 3.86 g/cm and a tension of...
A stretched string has a mass per unit length of 3.86 g/cm and a tension of 25.2 N. A sinusoidal wave on this string has an amplitude of 0.137 mm and a frequency of 156 Hz and is traveling in the negative direction of an x axis. If the wave equation is of the form y(x,t) = ym sin(kx + ωt), what are (a) ym, (b) k, and (c) ω, and (d) the correct choice of sign in front of...
A stretched string has a mass per unit length of 3.91 g/cm and a tension of...
A stretched string has a mass per unit length of 3.91 g/cm and a tension of 16.7 N. A sinusoidal wave on this string has an amplitude of 0.126 mm and a frequency of 78.0 Hz and is traveling in the negative direction of an x axis. If the wave equation is of the form y(x,t) = ym sin(kx + ωt), what are (a) ym, (b) k, and (c) ω, and (d) the correct choice of sign in front of...
1. A uniform horizontal beam OA, of length a and weight w per unit length, is...
1. A uniform horizontal beam OA, of length a and weight w per unit length, is clamped horizontally at O and freely supported at A. The transverse displacement y of the beam is governed by the differential equation d2y El dx2 w(a x)- R(a - x) where x is the distance along the beam measured from O, R is the reaction at A, and E and I are physical constants. At O the boundary conditions are dy (0) = 0....
1. The total kinetic energy of the vibrating string is given by the integral (a) Why...
1. The total kinetic energy of the vibrating string is given by the integral (a) Why does this integral give kinetic energy? (b) The potential energy V(t) of a stretched string originates in the work done against the tension T when as a result of its displacement, the string becomes longer. Show that (c) Use the series expression (3.16b if Nettel) to show that the total energy can be written as a sum over normal mode terms, with no cross-terms...
A string of length L stretched and is subjected to a tension of T. The thickness...
A string of length L stretched and is subjected to a tension of T. The thickness of the string is not uniform, and therefore, its linear density varies according to: µ = µo + k x, where x is distance from the left side of the string, µo and k are constants. (µo is in units of kg/m, and k in units of kg/m-2). Determine how long does it take for a wave to travel from one end to the...
If the mass per unit length of a violin string was quadrupled without changing the string's...
If the mass per unit length of a violin string was quadrupled without changing the string's tension, the speed with which a wave (produced by the player's bowing action) travels on that string would -become four times its former value. -become one half of its former value. -become two times its former value. -become one quarter of its former value. -not change.
A tension FT is applied to a wire with mass per unit length μ and length...
A tension FT is applied to a wire with mass per unit length μ and length L. When struck, it vibrates at its fundamental frequency f1. The wire is then removed and stretched to twice its original length 2L. If the same tension is applied to the stretched wire, what will be its new fundamental frequency?
A uniform string of length L = 1 is described by the one-dimensional wave equation au...
A uniform string of length L = 1 is described by the one-dimensional wave equation au dt2 dx where u(x,t) is the displacement. At the initial moment t = 0, the displacement is u(x,0) = sin(Tt x), and the velocity of the string is zero. (Here n = 3.14159.) Find the displacement of the string at point x = 1/2 at time t = 2.7.
A string of length L, mass per unit length mu, and tension T is vibrating at its fundamental frequency. What effect will the following have on the fundamental frequency? The length of the string is doubled, with all other factors held constant. The mass per unit length is doubled, with all other factors held constant. The tension is doubled, with all other factors held constant.
1. A uniform horizontal beam OA, of length a and weight w per unit length, is clamped horizontally at O and freely supported at A. The transverse displacement y of the beam is governed by the differential equation d2y El dx2 w(a x)- R(a - x) where x is the distance along the beam measured from O, R is the reaction at A, and E and I are physical constants. At O the boundary conditions are dy (0) = 0....
1. The total kinetic energy of the vibrating string is given by the integral (a) Why does this integral give kinetic energy? (b) The potential energy V(t) of a stretched string originates in the work done against the tension T when as a result of its displacement, the string becomes longer. Show that (c) Use the series expression (3.16b if Nettel) to show that the total energy can be written as a sum over normal mode terms, with no cross-terms...
A uniform string of length L = 1 is described by the one-dimensional wave equation au dt2 dx where u(x,t) is the displacement. At the initial moment t = 0, the displacement is u(x,0) = sin(Tt x), and the velocity of the string is zero. (Here n = 3.14159.) Find the displacement of the string at point x = 1/2 at time t = 2.7.
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