Question

Find (a) the amplitude, (b) the wavelength, (c) the period, and (d) the speed of a wave whose displacement is given by y= 1.5 cos( 0.68 x+ 37 t), where x and y are in cm and t is in seconds.

Answer 1

Answer with Step-by-step explanation:

We are given that displacement of wave

$y=1.5cos(0.68x+37t)$

Where y in cm  and t in sec.

a.Compare it with

$y=Acos(kx+\omega t)$

Amplitude of wave=A

We get A=1.5

Amplitude=A=1.5  cm

b.k=0.68

$\frac{2\pi}{\lambda}=0.68$

$\lambda=\frac{2\times 3.14}{0.68}=9.2 cm$

Using $\pi=3.14$

Wavelength of the wave=9.2 cm

c.Period=$\frac{2\pi}{T}=\omega$

$\frac{2\pi}{T}=37$

$T=\frac{2\times 3.14}{37}=0.17 s$

The period of the wave=0.17 s

Speed of the wave=$\nu \lambda=\frac{\lambda}{T}=\frac{9.2}{0.17}$

Speed of the wave=54.1 cm/s