A transverse wave on a string is described by . Where are in cm and in seconds. The least distance between the two

Question

A transverse wave on a string is described by $y = 3 \sin (36 t + 0.018 x + \frac{π}{4})$ . Where $x, y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is ______ cm. (Nearest integer) ( $π = 3.14$ ) [2026]

Smart Achievers · Accepted Answer

(349)

$y = 3 \sin (36 t + 0.018 x + \frac{π}{4})$

$Comparing with the standard equation$

$y = A \sin (ω t \pm k x + ϕ)$

$λ = \frac{2 π}{k} = \frac{2 \times 3.14}{0.018} = \frac{6.28}{0.018}$

$λ = 348.9 cm$

$Nearest integer=349 cm$

Solution

Q.
A transverse wave on a string is described by $y = 3 \sin (36 t + 0.018 x + \frac{π}{4})$ . Where $x, y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is ______ cm. (Nearest integer) ( $π = 3.14$ ) [2026]

Ans.
(349)

$y = 3 \sin (36 t + 0.018 x + \frac{π}{4})$

$Comparing with the standard equation$

$y = A \sin (ω t \pm k x + ϕ)$

$λ = \frac{2 π}{k} = \frac{2 \times 3.14}{0.018} = \frac{6.28}{0.018}$

$λ = 348.9 cm$

$Nearest integer=349 cm$

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Solution

Q. A transverse wave on a string is described by y=3sin(36t+0.018x+π4). Where x, y are in cm and t in seconds. The least distance between the two successive crests in the wave is ______ cm. (Nearest integer) (π=3.14) [2026]

Ans. (349) y=3sin(36t+0.018x+π4) Comparing with the standard equation y=Asin(ωt±kx+ϕ) λ=2πk=2×3.140.018=6.280.018 λ=348.9 cm Nearest integer=349 cm

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Q.
A transverse wave on a string is described by $y = 3 \sin (36 t + 0.018 x + \frac{π}{4})$ . Where $x, y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is ______ cm. (Nearest integer) ( $π = 3.14$ ) [2026]

Ans.
(349)

$y = 3 \sin (36 t + 0.018 x + \frac{π}{4})$

$Comparing with the standard equation$

$y = A \sin (ω t \pm k x + ϕ)$

$λ = \frac{2 π}{k} = \frac{2 \times 3.14}{0.018} = \frac{6.28}{0.018}$

$λ = 348.9 cm$

$Nearest integer=349 cm$