Answer to Question #227690 in Physics for Mosses07

Question

A wave traveling along a string is described by
f(x,t)=asin(πbx+qt),
with a = 35 mm , b = 0.33 m−1 , and q = 10.47 s−1.
(a)Calculate the amplitude of the wave
(b)Calculate the wavelength of the wave.
(c)Calculate the period of the wave.
(d)Calculate the speed of the wave.

Answer 1

A wave traveling along a string is described by with a = 35 mm , b = 0.33 m−1 , and q = 10.47 s−1.

$$f(x,t)=A\sin(kx+\omega t)\\=0.035\sin(0.33\pi x+0.47t)$$

(a) The amplitude of the wave

$$A=0.035\:\rm m$$

(b) The wavelength of the wave

$$\lambda=\frac{2\pi}{k}=\frac{2\pi}{0.33\pi}=6.1\:\rm m$$

(c) The period of the wave

$$T=\frac{2\pi}{\omega}=\frac{2\pi}{0.47}=13.4\:\rm s$$

(d) The speed of the wave

$$v=\lambda/T=6.1/13.4=0.46\:\rm m/s$$