A transverse wave on a string is described by the following wave function. where

Question

A transverse wave on a string is described by the following wave function.

where x and y are in meters and t is in seconds.

A transverse wave on a string is described by the following wave function. y = 0.105 sin where x and y are in meters and t is in seconds. Determine the transverse speed at t = 0.290 s for an element of the string located at x = 1.50 m. Determine the transverse acceleration at t = 0.290 s for an element of the string located at x = 1.50 m. What is the wavelength of this wave? What is the period of this wave? What is the speed of propagation of this wave?

Explanation / Answer

given that y=0.105*sin[(pi*x/12)+(5*pi*t)]...

1) velocity is v=dy/dt=1.65*cos[(pi*x/12)+(5*pi*t)]..

at t=0.29 sec and x=1.5m

v=0.386 m/sec...

2) aqccelaration a=dv/dt=25.2 m/sec^2...
3) wavelength lamda=2*pi/k=2*3.142/(pi/12)=24 m

4)period is T=2*pi/w=2*pi/5*pi=0.4

5)speed =v=w/k=1.527 m/sec

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