Question

A sinusoidal wave moving along a string is shown twice below, as crest A travels in the positive direction of an x axis by distance d = 1.5 cm in 4.4 ms. The tick marks along the axis are separated by 3.0 cm; height

H = 6.00 mm.

The wave equation is of the form below.

y(x, t) = y_m sin(kx ± ωt)

(a) What is y_m?
mm

(b) What is k?
rad/m

(c) What is ω?
rad/s

(d) What is the correct choice of sign in front of ω?

+−    

Answer 1

$t = 4.4 ms = 4.4\times 10^{-3} s$

$H = 6.0 mm = 6.0\times 10^{-3} m$

wave speed is $v = \frac{d}{t} = \frac{0.015 m}{4.4\times 10^{-3}s}$

$v =3.409 \frac{m}{s}$

(a)

$y_{m} = \frac{H}{2} = \frac{6.0 mm}{2}$

$y_{m} = \frac{6.0 mm}{2}$

(b)

wave length $\lambda = 4x$

$\lambda = 4\times 0.03 m$

$\lambda = 0.12 m$

$k = \frac{2\pi }{\lambda}$

$k = \frac{2\pi }{0.12 m}$

$k = 16.667\pi \frac{rad}{m}$

$k = 52.36\frac{rad}{m}$

(c)

$\omega = vk$

$\omega = 3.409 \frac{m}{s}\times 52.36 \frac{rad}{s}$

$\omega = 178.5 \frac{rad}{s}$

(D)

the wave move +x direction, the wave equation is $y = y_{m}sin\left ( kx-\omega t \right )$

Ans ===> (-)