# Chapter 15 Homework Mechanical Waves Qu. 1 A fisherman notices

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```					                             Chapter 15 Homework

Mechanical Waves

Qu. 1 A fisherman notices that his boat is moving up and down periodically,
owing to waves on the surface of the water. It takes 2.5s for the boat to
travel from it’s highest point to it’s lowest, a total distance of 0.62m. The
fisherman sees that the wave crests are spaced 6m apart.

a) How fast are the waves traveling?                (Ans: 1.2 m/s)
b) What is the amplitude of each wave?              (Ans 0.31 m)
c) If the total vertical distance traveled by the boat were 0.3m, but the
other data remained the same, how would the answers to parts a) and
be affected?
(Ans: velocity is unaffected but the amplitude is halved).
d) Would you expect that the motion of the boat would be purely
vertical? (Ans: not necessarily because the boat is not a point mass).

Qu. 2 A certain transverse wave is described by

y(x,t) = 6.5 Cos 2π ( (x/28 cm) – (t/0.036 s)        mm

Determine the wave’s

a)   amplitude                  (Ans: 6.5 mm)
b)   wavelength                 (Ans: 28 cm)
c)   Period                     (Ans: 0.036 s)
d)   velocity                    (Ans: 7.77 m/s
e)   direction of propagation    (Ans: left to right)
Qu. 3 Transverse waves on a string have wave speed 8 m/s, amplitude 0.07m
and wavelength 0.32m. The waves travel the negative x direction and at t=0
the x=0 end of the string has it’s maximum upward displacement.

a) Find the frequency, period and wave number for these waves.
Ans: f = 25 Hz, T = 0.04 s, k = 19.63)

b) Write the wave function describing the wave.
(Ans: y(x,t) = 0.07Sin 2π ( (x/0.32) + (t/0.04) + 1/4)           m

c) Find the transverse displacement of a particle at x = 0.36m at a time t
= 0.15s (Ans: y = 0.05m)

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