For a transverse wave traveling along a straight line, the distance between two peaks (crests) is 5 , while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in <math><mi mathvariant="normal">A</mi><mo>→</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">V</mi><mo>;</mo><mrow><mi mathvariant="normal"></mi></mrow><mi mathvariant="normal">B</mi><mo>→</mo><mi mathvariant="normal">I</mi></math> ) of the waves are:

(n) λ=5 (n, m) : Integers2m+12λ=32⇒3/25=2m+12n⇒3n=10m+5N, m are integers.So, m=1, n=5, λ=1m=4n=15λ=13m=7n=25λ=15

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Physics Class 12th Waves Physics NCERT Exemplar Solutions Class 12th Chapter Fifteen

For a transverse wave traveling along a straight line, the distance between two peaks (crests) is 5
, while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in $A \to I V; B \to I$ ) of the waves are:

Option 1 -

1,3,5...

Option 2 -

1/1, 1/3,1/5....

Option 3 -

1/2, 1/4, 1/6......

Option 4 -

1,2,3....

2 Views | Posted 2 months ago

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 2

Detailed Solution:

(n) $λ = 5$

$(n, m)$ : Integers

$\begin{array}{r} (\frac{2 m + 1}{2}) λ = \frac{3}{2} \\ \Rightarrow \frac{3 / 2}{5} = \frac{2 m + 1}{2 n} \\ \Rightarrow 3 n = 10 m + 5 \end{array}$

$N, m$ are integers.

So, $m = 1, n = 5, λ = 1$

$\begin{array}{l} m = 4 & n = 15 & λ = \frac{1}{3} \\ m = 7 & n = 25 & λ = \frac{1}{5} \end{array}$

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$\Rightarrow v (\frac{1}{λ_{1}} - \frac{1}{λ_{2}}) = \frac{10}{3}$

$\Rightarrow$ $V$ $=$ $\frac{10}{3}$ $\times$ $\frac{λ_{1} λ_{2}}{λ_{2} - λ_{1}}$ $=$ $\frac{10}{3}$ $\times$ $\frac{4.08 \times 4.16}{. 08}$ $=$ $\frac{10}{3}$ $\times$ $\frac{408 \times 4.16}{8}$ $=$ $7$ $0$ $7$ $.$ $2$ $m$ $/$

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For a transverse wave traveling along a straight line, the distance between two peaks (crests) is 5
, while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in $A \to I V; B \to I$ ) of the waves are:

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For a transverse wave traveling along a straight line, the distance between two peaks (crests) is 5 , while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in A→IV;B→I ) of the waves are:

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For a transverse wave traveling along a straight line, the distance between two peaks (crests) is 5
, while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in $A \to I V; B \to I$ ) of the waves are: