The equation of the progressive wave is ...

The equation of the progressive wave is y =a `sin pi (nt -(x)/(5))` the ratio maximum paritcle velocity to wave velocity is

`(pi a)/(5)`

`(2pi a)/(5)`

`(3pi a)/(5)`

`(4pia)/(5)`

Text Solution

Verified by Experts

The correct Answer is:

We have
y = a sin `2pi(nt-(x)/(5))`
here vi is wave velocity
`u_(max)/(v)=(2pia)/(lambda)=(2pia)/(5)[therefore k=(2pi)/(lambda)]`
`lambda=(2pi)/(k)=(2pi)/(2pi//5)=5`

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The equation of travelling wave is y=a sin 2pi (pt-(x)/(5)) Then the ratio of maximum particle velocity to wave velocity is

`(pi a )/(5) `

`2sqrt(5pia ) `

`(2pi a )/(5) `

`(2pi a )/(sqrt(5))`

The equation of a travelling wave is, Y = A sin 2pi (pt-x//5) Then the ratio of maximum particle velocity to wave velocity is,

`(piA)/(5)`

`2sqrt(5pi A)`

`(2piA)/(5)`

`(2piA)/(sqrt5)`

The equation of a transverse wave is y=asin2pi[t-(x//5)] , then the ratio of maximum particle velocity and wave velocity is

`(2pia)/(sqrt(5))`

`(2pia)/(5)`

`(a)/(5)`

`2piasqrt(5)`