To practice Problem-Solving Strategy 15.1 Mechanical Waves. Waves on a string are described by the following general equation y(x, t)=Acos(kx−ωt). A transverse wave on a string is traveling in the +x direction with a wave speed of 8.25 m/s , an amplitude of 5.50×10−2 m , and a wavelength of 0.540 m . At time t=0, the x=0 end of the string has its maximum upward displacement. Find the transverse displacement y of a particle at x = 1.51 m and t = 0.150 s .

The transverse displacement is      

Explanation:

 From the question we are told that

     The generally equation for the mechanical wave is

     The speed of the transverse wave is

     The amplitude of the transverse wave is

     The wavelength of the transverse wave is

      At t= 0.150s , x = 1.51 m

 The angular frequency of the wave is mathematically represented as

Substituting values  

The propagation constant k is mathematically represented as

Substituting values

Substituting values into the equation for mechanical waves

diagram is missing, but i will try to explain your doubt.

answer:

amplitude is the maximum displacement or distance moved on a point of a vibrating body or wave measured from its equilibrium position.it is equal to half the length of vibration path.

v=ir = 3x15 =45 v