The equation of a progressive wave is given by y = 5 sin $(100 π t - 0.4 π x)$ where y and x are in m and t is in s
(1) The amplitude of the wave is 5 m.
(2) The wavelength of the wave is 5 m.
(3) The frequency of the wave is 50 Hz.
(4) The velocity of the wave is 250 m s^-1
Which of the following statements are correct?

(1), (2) and (3)

(2) and (3)

(1) and (4)

All are correct

Solution

All are correct

The equation of a given progressive wave is

y = 5 sin $(100 πt - 0.4 πx)$ ....(i)

The standard equation of a progressive wave is

y = a sin ( ωt $-$ kx )

Comparing equation (i) and (ii)

α = 5 m

ω = 100 $π$ rad s^-1

k = 0.4 $π m^{- 1}$

(1) Amplitude of the wave, a = 5 m

(2) Wavelength of the wave,

$λ = \frac{2 π}{k}$

= $\frac{2 π}{0.4 π}$

λ = 50 m

(3) Frequency of he wave

$v = \frac{ω}{2 π}$

= $\frac{100 π}{2 π}$

v = 50 Hz

(4) Velocity of the wave

v = v λ

= ( 50 s^-1 ) (5 m)

v = 250 ms^-1

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