Answer to Question #161227 in Physics for Raj

Question

4. A transverse traveling wave on a cord is represented by y(x,t)=0.48 sin (4x + 10πt) where y and x are in meters and t in seconds

a) For this wave determine the wavelength, frequency, phase velocity (magnitude and direction), amplitude, maximum and minimum transverse speeds of particles of the cord.

b) What is the minimum length of the cord required for a standing wave to be formed when this wave meets its neflection

c) Winte the equation representne the standine wave. What is the amplitude or vibration for a particle of the sunne located at x = 0.15 m ?

Answer 1

a)

$$\lambda=\frac{2\pi}{4}=1.57\ m\\ f=\frac{10\pi}{2\pi}=5\ Hz\\ v=(1.57)5=7.85\frac{m}{s}\\\text{A positive sign means the wave is traveling in the -x direction. }\\ A=0.48\ m\\$$

$$v_{max}=0.48(10\pi)=15.08\frac{m}{s}\\v_{min}=0\frac{m}{s}$$

b)

$$L=\pi=3.14\ m$$

c)

$$y(x,t)=[2(0.48)\sin(4x)]\cos(10\pi t)\\A'=[2(0.48)\sin(4(0.15))]=0.54\ m$$