End of chapter exercises
A wave travels along a string at a speed of 1,5 m·s^{−1}. If the frequency of the source of the wave is 7,5 Hz, calculate:

the wavelength of the wave

the period of the wave
a)
$v=\lambda \cdot f$ 
$\lambda =\frac{v}{f}$ 
$\lambda =\frac{1,5}{7,5}$ 
$\lambda =0,2\text{m}$ 
b)
$T=\frac{1}{f}$ 
$T=\frac{1}{7,5}$ 
$T=1,33\text{s}$ 
Water waves crash against a seawall around the harbour. Eight waves hit the seawall in 5 s. The distance between successive troughs is 9 m. The height of the waveform trough to crest is 1,5 m.

How many complete waves are indicated in the sketch?

Write down the letters that indicate any TWO points that are:

in phase

out of phase

Represent ONE wavelength.


Calculate the amplitude of the wave.

Show that the period of the wave is 0,625 s.

Calculate the frequency of the waves.

Calculate the velocity of the waves.
a) Three complete waves are shown.
bi) Any one of the following pairs of points: BD, BF, DF, CE, CG, EG, AH
ii) Any one of the following pairs of points: AB, AC, AD, AE, AF, AG, BC, BE, BG, BH, CD, CF, CH, DE, DG, DH, EF, EH, FG, FH, GH
iii) Any one of the following pairs of points: BD, DF, CE or EG
c) 0,75 m (We are given the height, the amplitude is half the height)
d) 8 waves in 5 s
e)
$f=\frac{1}{T}=\frac{1}{0,625}=1,60\text{Hz}$
f)
$v=f\lambda =(1,60)\left(10\right)=16,0\text{m}\cdot {\text{s}}^{1}$