Question

A transverse sinusoidal wave is moving along a string in the positive direction of an x axis with a speed of 87 m/s. At t=0, the string particle at x = has a transverse displacement of 4.2 cm from its equilibrium position and is not moving. The maximum transverse speed of the string particle at x = is 17 m/s. (a) What is the frequency of the wave? (b) What is the wavelength of the wave? If the wave equation is of the form yix, t) - Yo sin(kort ut + o), what are (c) Ym. (d)k, (e), (1) , and (9) the correct choice of sign in front of ? Units Hz units units i (a) Number 64.45253248 (b) Number (e) Number (d) Number (e) Number 1 (1) Number Units Units Units

Answer 1

Lets look at the questions one by one keeping in mind all the given data-

Giren, y = 4.2 cm. at x=0, t=0 V = 87 m/s Vm= 17 m/s. (a) so, the frequency of the ware is farver og -video -866-84Hz: 17X100 -4.2 164.41 Hz. (C) The wavelleyth is - 4: 8h - 145 m From the given foom of the ware equation y (art) = ymson (kx twt +O) subststelling y : 4.2 cm. - Cd. x=0,t=0 we get ym 10.042 m.] The wave number 1:2 = at - 4.65 m. an 1:35

(e. The angular relocity is given by. - Um Ym 17 0.042 (f.) - 404.76 rad/ See. The phase of the ware function using condition given before which is the y = 4.20m. x=0,t=0 0.042 = 0.042 sia CA65(0) + 404.76 +02 solning for. sind =1 we get 10 = 7 Rodian or goo . The correct choice of Sign in front of w is minus because the wave is shown bravelling to positive direction of x-axis. C.