The equation of stationary wave is, Which of the following is not correct?

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Q.
The equation of stationary wave is: [2024]

$y = 2 a \sin (\frac{2 πnt}{λ}) \cos (\frac{2 πx}{λ}) .$

Which of the following is not correct

1 The dimensions of $x$ is $[L]$

2 The dimensions of $n t$ is $[L]$

3 The dimensions of $n$ is $[L T^{- 1}]$

4 The dimensions of $n / l$ is $[T]$

Ans.
(4)

$y = 2 a \sin (\frac{2 πnt}{λ}) \cos (\frac{2 πx}{λ})$

(i) $[x] = L$

(ii) $[\frac{2 πnt}{λ}] = 1 \Rightarrow [n t] = 1 \cdot [λ] = L$

(iii) $[n t] = L \Rightarrow [n] = L T^{- 1}$

(iv) $[\frac{n}{λ}] = \frac{L T^{- 1}}{L} = T^{- 1}$

Solution

Q.
The equation of stationary wave is: [2024]

$y = 2 a \sin (\frac{2 πnt}{λ}) \cos (\frac{2 πx}{λ}) .$

Which of the following is not correct

1 The dimensions of $x$ is $[L]$

2 The dimensions of $n t$ is $[L]$

3 The dimensions of $n$ is $[L T^{- 1}]$

4 The dimensions of $n / l$ is $[T]$

Ans.
(4)

$y = 2 a \sin (\frac{2 πnt}{λ}) \cos (\frac{2 πx}{λ})$

(i) $[x] = L$

(ii) $[\frac{2 πnt}{λ}] = 1 \Rightarrow [n t] = 1 \cdot [λ] = L$

(iii) $[n t] = L \Rightarrow [n] = L T^{- 1}$

(iv) $[\frac{n}{λ}] = \frac{L T^{- 1}}{L} = T^{- 1}$

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Solution

Q. The equation of stationary wave is: [2024] y=2asin(2πntλ)cos(2πxλ). Which of the following is not correct

1 The dimensions of x is [L]

2 The dimensions of nt is [L]

3 The dimensions of n is [LT-1]

4 The dimensions of n/l is [T]

Ans. (4) y=2asin(2πntλ)cos(2πxλ) (i) [x]=L (ii) [2πntλ]=1⇒[nt]=1·[λ]=L (iii) [nt]=L⇒[n]=LT-1 (iv) [nλ]=LT-1L=T-1

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Q.
The equation of stationary wave is: [2024]

$y = 2 a \sin (\frac{2 πnt}{λ}) \cos (\frac{2 πx}{λ}) .$

Which of the following is not correct

1 The dimensions of $x$ is $[L]$

2 The dimensions of $n t$ is $[L]$

3 The dimensions of $n$ is $[L T^{- 1}]$

4 The dimensions of $n / l$ is $[T]$

Ans.
(4)

$y = 2 a \sin (\frac{2 πnt}{λ}) \cos (\frac{2 πx}{λ})$

(i) $[x] = L$

(ii) $[\frac{2 πnt}{λ}] = 1 \Rightarrow [n t] = 1 \cdot [λ] = L$

(iii) $[n t] = L \Rightarrow [n] = L T^{- 1}$

(iv) $[\frac{n}{λ}] = \frac{L T^{- 1}}{L} = T^{- 1}$