Question #147729
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.
1
Expert's answer
2020-11-30T14:51:50-0500

(i) The wave velocity is


v=λf=512=60msv=λf=5⋅12=60\frac{m}{s}

(ii) The three other positions of the crest are


x1=x+λ=3+5=8 m,x2=x+2λ=3+25=13 mx_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=λv=f1=0.083 s.t= \frac{\lambda}{v} = f^{-1} =0.083\ s.

(iv) The equation is


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


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