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:

Ask & Answer Question

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 -

$1.5 m$

2 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | 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, $m = 1, n = 5, λ = 1$

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

(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>

0 Upvotes 0 Downvotes

Get authentic answers from experts, students and alumni that you won't find anywhere else

On Shiksha, get access to

65k Colleges
1.2k Exams
682k Reviews
1800k Answers

Community GuidelinesUser Points System

QuestionsDiscussionsTags

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:

1 Answer

Learn more about...

Most viewed information

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

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:

1 Answer

Learn more about...

Most viewed information

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question

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: