A transverse wave travelling on a taut string is represented by -y-0-01 sin 2- 10t-x- y and x are in meters and t in seconds- Then

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Wave Speed expression

A transverse ...

Question

A transverse wave travelling on a taut string is represented by :
$y = 0.01 sin 2 π (10 t - x) \to y$ and $x$ are in meters and $t$ in seconds. Then
Closest points on the string which differ in phase by $60^{\circ}$ are $(1 / 6) m$ apart.

The speed of the wave is $10 m/s$
The phase of a certain point on the string changes by $120^{\circ}$ in $(1 / 20)$ seconds.

Maximum particles velocity is $π / 4 m/s .$

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Solution

The correct option is B The speed of the wave is $10 m/s$
$y = 0.01 sin [2 π (10 t - x)]$

$\Rightarrow y = 0.01 sin [2 π t - 2 π x]$

Comparing with standard equation, we get
$ω = 20 π, k = 2 π$

Wave velocity:

$v = \frac{ω}{k} = \frac{20 π}{2 π} = 10 m/s$

$Δ ϕ = k Δ x, given Δ ϕ = 60^{\circ} = \frac{π}{5} m/s$

$\frac{π}{3} = 2 π Δ x$

$\Rightarrow Δ x = \frac{1}{6} m$

$(v_{p})_{-max} = ω A = 20 π \times 0.01 = \frac{π}{5} m/s$

$Δ ϕ_{t} = ω Δ t = 20 π \times \frac{1}{20} = π$

so in time $\frac{1}{20} s$ , phase changes by and not $120^{\circ}$

Hence, $(A)$ and $(B)$ are the correct options.

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