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When a wave transverses in a medium, the...

When a wave transverses in a medium, the displacement of a particle located at distance x at time t is given by `y=a sin (bt-cx)` where a, b and c are constants of the wave. The dimension of `b//c` are same as that of:

A

wave velocity

B

wave length

C

wave amplitude

D

wave frequency

Text Solution

Verified by Experts

The correct Answer is:
A
bt and cx are arguments of sine thus they are dimensionless
`bt = M^(0)L^0T^0" "cx = M^(0)L^(0)T^(0)`
`b= M^(0)L^(0)T^(-1)" "c = M^(0)L^(-1) T^(0)`
`b//c= ([T^(-1)])/([L^(-1)])= [LT^(-1)] = v = ` wave velocity
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Knowledge Check

  • When a wave traverses a medium, the displacement of a particle located at 'x' at a time 't' is given by y = a sin (bt - cx) , where a,b and c are constants of the wave, which of the following is a quantity with dimensions?

    A
    `y//a`
    B
    `bt`
    C
    `cx`
    D
    `b//c`

  • When a wave traverses a medium , the displacement of a particle located at x at a time t is given by y=asin(bt-cx), where a,b and c are constants of the wave , which of the following is a quantity with dimensions ?

    A
    y/a
    B
    bt
    C
    cx
    D
    b/c

  • The velocity v of a particle at time t is given by v=at+b/(t+c) , where a, b and c are constants. The dimensions of a, b, c are respectively :-

    A
    `LT^(-2)`, L and T
    B
    `L^(2)`, T and `LT^(2)`
    C
    `LT^(2)`, LT and L
    D
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