Answer to Question #162898 in Physics for Hazel

Question

Your cousin is playing with the clothesline. He unties one end, holds it tight, and wiggles the end up and down sinusoidally with f=2.00 Hz, A=0.075m and v=12.0m/s at time t=0, the end has zero displacement and is moving in the +y-direction. Assume that no wave bounces back from the far end to muddle up the pattern.

A. Find the amplitude, angular frequency, period, wavelength, and wave number of the wave.

B. Write its corresponding wave function

Answer 1

A.

$$A=0.075\ m.$$

We can find the angular frequency as follows:

$$\omega=2\pi f=2\pi\cdot2.0\ Hz=12.6\ \dfrac{rad}{s}.$$

We can find the period as follows:

$$T=\dfrac{1}{f}=\dfrac{1}{2.0\ Hz}=0.5\ s.$$

We can find the wavelength from the wave speed equation:

$$\lambda=\dfrac{v}{f}=\dfrac{12.0\ \dfrac{m}{s}}{2.0\ Hz}=6.0\ m.$$

We can find the wave number as follows:

$$k=\dfrac{2\pi}{\lambda}=\dfrac{2\pi}{6.0\ m}=1.05\ m^{-1}.$$

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

$$y(x,t)=A\ cos2\pi\ (\dfrac{x}{\lambda}- \dfrac{t}{T}),$$ $$y(x,t)=(0.075\ m)\cdot cos2\pi\ (\dfrac{x}{6.0\ m}- \dfrac{t}{0.5\ s}),$$ $$y(x,t)=0.075 \cdot cos(1.05x- 12.6t).$$