Answer to Question #162891 in Physics for Hazel

Question

The transverse waves has the following characteristics:

v=8.00m/s, A=0.0700m, and y=0.320m. The waves travel in the –x-direction, and at t=0 the x=0 end of the string has zero displacement and is moving in the +y-direction.

A. Calculate the frequency, period and wave number and angular frequency of these waves;

B. Write a wave function describing the wave.

Answer 1

(A) We can find the frequency from the wave speed equation:

$$v=f\lambda,$$ $$f=\dfrac{v}{\lambda}=\dfrac{8.0\ \dfrac{m}{s}}{0.320\ m}=25\ Hz.$$

The period can be found as follows:

$$T=\dfrac{1}{f}=\dfrac{1}{25\ Hz}=0.04\ s.$$

Wave number can be found as follows:

$$k=\dfrac{2\pi}{\lambda}=\dfrac{2\pi}{0.320\ m}=19.6\ m^{-1}.$$

The angular frequency can be found as follows:

$$\omega=2\pi f=2\pi\cdot25\ Hz=157\ \dfrac{rad}{s}.$$

(B) The general wave function describing the transverse waves can be written as follows:

$$y(x,t)=A\ cos2\pi\ (\dfrac{x}{\lambda}\mp \dfrac{t}{T}),$$

here sign minus corresponds to the wave traveling in +$x$-direction and sign plus correspond to the wave traveling in -$x$-direction.

Therefore, we get:

$$y(x,t)=0.07\cdot cos2\pi\cdot (\dfrac{x}{0.320}+ \dfrac{t}{0.04}).$$