The equation of a wave travelling on a string is y = sin [20 x + 10 t], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is : [2025]

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Solution

Q.
The equation of a wave travelling on a string is y = sin [20 $π$ x + 10 $π$ t], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is : [2025]

1 5.0 cm

2 20 cm

3 10 cm

4 2.5 cm

Ans.
(1)

$k = 20 π = \frac{2 π}{λ} \Rightarrow λ = 10 cm$

Minimum distance between 2 points having same speed is $\frac{λ}{2}$ .

Minimum distance $= \frac{λ}{2} = 5 cm$

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