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

`(2\pi)/(\lambda)=0.68`

`\lambda=(2* 3.14)/(0.68)=9.2 cm`

Using
`\pi=3.14`

Wavelength of the wave=9.2 cm

c.Period=
`(2\pi)/(T)=\omega`

`(2\pi)/(T)=37`

`T=(2* 3.14)/(37)=0.17 s`

The period of the wave=0.17 s

Speed of the wave=
`\\u \lambda=(\lambda)/(T)=(9.2)/(0.17)`

Speed of the wave=54.1 cm/s