The equation of a transverse wave travelling along a string is , where x is in the mm and t is in second. The velocity of the wave is [2025]

Question

The equation of a transverse wave travelling along a string is $y (x, t) = 4.0 \sin [20 \times 10^{- 3} x + 600 t] mm$ , where x is in the mm and t is in second. The velocity of the wave is [2025]

Smart Achievers · Accepted Answer

(3)

$y = 4 \sin (20 \times 10^{- 3} x + 600 t)$

Here, $ω$ = 600 and k = $20 \times 10^{- 3}$

$∴ v = \frac{ω}{k} = \frac{600}{20 \times 10^{- 3}}$

$= 30 \times 10^{+ 3} mm / s = 30 m / s$

and direction is towards –ve x-axis

$∴$ v = – 30 m/s

Solution

Q.
The equation of a transverse wave travelling along a string is $y (x, t) = 4.0 \sin [20 \times 10^{- 3} x + 600 t] mm$ , where x is in the mm and t is in second. The velocity of the wave is [2025]

1 + 30 m/s

2 – 60 m/s

3 – 30 m/s

4 + 60 m/s

Ans.
(3)

$y = 4 \sin (20 \times 10^{- 3} x + 600 t)$

Here, $ω$ = 600 and k = $20 \times 10^{- 3}$

$∴ v = \frac{ω}{k} = \frac{600}{20 \times 10^{- 3}}$

$= 30 \times 10^{+ 3} mm / s = 30 m / s$

and direction is towards –ve x-axis

$∴$ v = – 30 m/s

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