Chapter 14 - Waves and Sound - Problems and Conceptual Exercises - Page 491: 5

a) $d_w=0.607m$ b) $d_t=1.08m$ c) the answer in (a) is unchanged; the answer in (b) is halved.

(a) We know that $d_w=v\times t$ $\implies d_w=f\lambda\times t$ We plug in the known values to obtain: $d_w=(4.5Hz)(0.27m)(0.50s)$ $\implies d_w=0.607m$ (b) We can determine the required distance as follows: $d_t=4Aft$ We plug in the known values to obtain: $d_t=4(0.12m)(4.5Hz)(0.50s)$ $\implies d_t=1.08m$ (c) As the distance traveled by the peak wave doesn't depend on the amplitude, hence there will be no effect on part (a) (remains unchanged). On the other hand, for part (b), the distance traveled by the knot is directly proportional to the amplitude and when the amplitude is halved then the distance is halved as well.