y = 3 sin $π (\frac{t}{2} - \frac{x}{4})$ represents an equation of a progressive wave, where t is in second and x is in metre. The distance travelled by the wave in 5 s is

8 m

10 m

5 m

32 m

Solution

10 m

The given equation of a progressive wave is

y = 3 sin $π (\frac{t}{2} - \frac{x}{4})$

= 3 sin 2 $π (\frac{t}{4} - \frac{x}{8})$

The standard equation of a progressive wave is

y = y_o sin $2 π (\frac{t}{T} - \frac{x}{λ})$

Comparing these two equations, we get

T = 4 s , λ = 8m

∴ The velocity of wave,

v = $\frac{λ}{T}$

= $\frac{8}{4}$

⇒ v = 2 ms^-1

Distance travelled by wave in time t is

s = v t

⇒ s = 2 × 5

⇒ s = 10 m

Some More Questions From Waves Chapter

For Daily Free Study Material Join wiredfaculty