For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m , while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in m ) of the waves are

Question

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m , while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in m ) of the waves are (A) 1,2,3, ldots  (B) (1/2), (1/4), (1/6), ldots (C) 1,3,5, ldots (D) (1/1), (1/3), (1/5), ldots

Tardigrade Admin · Accepted Answer

Given T to C 1.5 m C to C 5 m T to C =(2 n 1+1) (λ/2) C to C=n2 λ (1.5/5)=((2 n 1+1)/2 n 2) ⇒ 3 n 2=10 n 1+5 n 1=1, n 2=5 arrow λ=1 n 1=4, n 2=15 arrow λ=1 / 3 n 1=7, n 2=25 arrow λ=1 / 5

Q. For a transverse wave travelling along a straight line, the distance between two peaks (crests) is $5 m,$ while the distance between one crest and one trough is $1.5 m$ . The possible wavelengths (in $m$ ) of the waves are

$1, 2, 3, \dots$

$\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \dots$

$1, 3, 5, \dots$

$\frac{1}{1}, \frac{1}{3}, \frac{1}{5}, \dots$

Given $T$ to $C 1.5 m$
$C$ to $C 5 m$
$T$ to $C = (2 n_{1} + 1) \frac{λ}{2}$
$C$ to $C = n_{2} λ$
$\frac{1.5}{5} = \frac{( 2 n _{1} + 1 )}{2 n _{2}}$
$\Rightarrow 3 n_{2} = 10 n_{1} + 5$
$n_{1} = 1, n_{2} = 5 \to λ = 1$
$n_{1} = 4, n_{2} = 15 \to λ = 1/3$
$n_{1} = 7, n_{2} = 25 \to λ = 1/5$

Q. For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5m, while the distance between one crest and one trough is 1.5m. The possible wavelengths (in m ) of the waves are

1,2,3,…

21​,41​,61​,…

1,3,5,…

11​,31​,51​,…