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 = 3m at time t, find three other positions of the crest at that instant.
(iii) What time later will there be another crest at x = 3m?
(iv) If the amplitude of the wave is 1.5 m , write the equation of the wave.

Answer 1

(i) The wave velocity is

$$v=\lambda f=5\cdot12=60\text{ m/s}.$$

(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

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

(iv) The equation is

$$y(t)=A\text{ sin}(2\pi t)$$