For a transverse wave traveling along a straight line, the distance between two peaks (crests) is <math> <mi mathvariant="normal">C</mi> <mo>→</mo> <mi mathvariant="normal">I</mi> </math> <math></math> , while the distance between one crest and one trough is <math></math> <math> <mi mathvariant="normal">D</mi> <mo>→</mo> <mi mathvariant="normal">I</mi> <mi mathvariant="normal">V</mi> </math> . 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> <math><mrow><mi mathvariant="normal"></mi></mrow></math> ) of the waves are:

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

For a transverse wave traveling along a straight line, the distance between two peaks (crests) is <math> <mi mathvariant="normal">C</mi> <mo>→</mo> <mi mathvariant="normal">I</mi> </math> <math></math>&nbsp;, while the distance between one crest and one trough is&nbsp;<math></math> <math> <mi mathvariant="normal">D</mi> <mo>→</mo> <mi mathvariant="normal">I</mi> <mi mathvariant="normal">V</mi> </math> . 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> <math><mrow><mi mathvariant="normal"></mi></mrow></math>&nbsp;) of the waves are:

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Physics NCERT Exemplar Solutions Class 11th Chapter Ten Wavelength and Frequency Physics Waves Physics Class 11th

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

Option 1 -

$C \to I$

Option 2 -

$D \to I I I$

Option 3 -

$5 m$

Option 4 -

$1.5 m$

5 Views | Posted 3 months ago

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1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

3 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, $m = 1, n = 5, λ = 1$

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

(n) <math> <mi>λ</mi> <mo>=</mo> <mn>5</mn> </math> <math></math><math></math> <math> <mo> (</mo> <mi mathvariant="normal">n</mi> <mo>, </mo> <mi mathvariant="normal">m</mi> <mo>)</mo> </math>  : Integers <math> <mtable columnalign="right"> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> <mi>λ</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi> </mi> <mo>⇒</mo> <mrow> <mi mathvariant="normal"> </mi> </mrow> <mfrac> <mrow> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </mrow> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi> </mi> <mo>⇒</mo> <mrow> <mi mathvariant="normal"> </mi> </mrow> <mn>3</mn> <mi>n</mi> <mo>=</mo> <mn>10</mn> <mi>m</mi> <mo>+</mo> <mn>5</mn> </mrow> </mtd> </mtr> </mtable> </math> <math></math> <math> <mi mathvariant="normal">N</mi> <mo>, </mo> <mi mathvariant="normal">m</mi> </math>  are integers.So, <math> <mi mathvariant="normal">m</mi> <mo>=</mo> <mn>1</mn> <mo>, </mo> <mrow> <mi mathvariant="normal"> </mi> </mrow> <mi mathvariant="normal">n</mi> <mo>=</mo> <mn>5</mn> <mo>, </mo> <mrow> <mi mathvariant="normal"> </mi> </mrow> <mi>λ</mi> <mo>=</mo> <mn>1</mn> </math> <math><mrow><mi mathvariant="normal"></mi></mrow><mrow><mi mathvariant="normal"></mi></mrow></math> <math> <mtable columnalign="left"> <mtr> <mtd> <mrow> <mi mathvariant="normal">m</mi> <mo>=</mo> <mn>4</mn> </mrow> </mtd> <mtd> <mrow> <mi mathvariant="normal">n</mi> <mo>=</mo> <mn>15</mn> </mrow> </mtd> <mtd> <mrow> <mi>λ</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mo>=</mo> <mn>7</mn> </mrow> </mtd> <mtd> <mrow> <mi mathvariant="normal">n</mi> <mo>=</mo> <mn>25</mn> </mrow> </mtd> <mtd> <mrow> <mi>λ</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </math>

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