Answer to Question #147729 in Physics for Portia

Question

The distance between two successive crest is 5 m at a frequency of 12 Hz.
(i) What is the wave velocity?
(ii) If there is a crest at x = 3 m at time t, find three other positions of the crest at that instant.
(iii) What time later will there be another crest at x = 3 m?
(iv) If the amplitude of the wave is 1.5 m, write the equation of the wave.

Answer 1

(i) The wave velocity is

$$v=λf=5⋅12=60\frac{m}{s}$$

(ii) The three other positions of the crest are

$$x_1=x+\lambda=3+5=8\text{ m},\\ x_2=x+2\lambda=3+2\cdot5=13\text{ m}$$

(iii) The time it will take is

$$t= \frac{\lambda}{v} = f^{-1} =0.083\ s.$$

(iv) The equation is

$$y(t)=1.5\sin(2π(12)t)=1.5\sin(24πt)$$