a string with linear density 3.0g/m isstreched along the positive axis with a te

Question

   a string with linear density 3.0g/m isstreched along the positive axis with a tension of 15n. one end ofthe string, at x=o, is tied to a hook that oscillates up and down(i.e. in the y-direction) at a frequency of 55 hz with a maximumdisplacement of 1.5 mm. at t-0s the hook is at y= 0.5 mm and movingupward. a)what is the wave speed on this string? b)what is the wavelength of the waves that are being excitedby the oscillations of the hook? c)write the equation for the displacement, D(x,t), of thetravelling wave. d) what is the displacement of the string at x= 0.20 m andt=35ms?    a string with linear density 3.0g/m isstreched along the positive axis with a tension of 15n. one end ofthe string, at x=o, is tied to a hook that oscillates up and down(i.e. in the y-direction) at a frequency of 55 hz with a maximumdisplacement of 1.5 mm. at t-0s the hook is at y= 0.5 mm and movingupward. a)what is the wave speed on this string? b)what is the wavelength of the waves that are being excitedby the oscillations of the hook? c)write the equation for the displacement, D(x,t), of thetravelling wave. d) what is the displacement of the string at x= 0.20 m andt=35ms?

Explanation / Answer

Let =linear density = 3g/m = (3*10^-3)kg/m Let =tension = 15N a) wave speed: velocity of wave = (/) ˜70.7m/s b)Let = wavelength Let k = wave number y=A*sin(t - kx) from info provided we know... 0.0005=0.0015*sin(0 - kx) We also know that velocity (which we solved for in (a), is/k) =2*55 Hz = 110 so 70.7= 110 / k    k ˜4.9 rad/meter We can finally solve for = 2 / k ˜ 1.28m c) D(x,t) means displacement from relaxed position, which is afunction of x position and t time D(x,t) = A*sin(t - kx) //where A=amplitude=max displacement,=angular velocity, rest you know i think D(0.20m ,0.035s) = 0.0015*sin(110* 0.035 - 4.9*0.20) ˜ -0.001489

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