A progressive wave is represented by y=12sin (. 5 t - 4 x .) cm . On this wave, how far away are the two points having a phase difference of 90° ?

Question

A progressive wave is represented by y=12sin (. 5 t - 4 x .) cm . On this wave, how far away are the two points having a phase difference of 90° ? (A) (π /2) cm (B) (π /4) c m (C) (π /8) cm (D) (π /16) cm

Tardigrade Admin · Accepted Answer

y=12 sin (.5t-4x.) Comparing in y=Asin (w t - k x) We have A=12, w=5 and k=4 (w t - k x)= phase difference =(π /2) ∴ |. 5 t - 4 x |. = (π /2) When t=0, 4x=(π /2) ∴ x=(π /8) cm

Q. A progressive wave is represented by $y = 12 s in (5 t - 4 x)$ $c m$ . On this wave, how far away are the two points having a phase difference of $9 0^{\circ}$ ?

$\frac{π}{2} c m$

$\frac{π}{4} c m$

$\frac{π}{8} c m$

$\frac{π}{16} c m$

$y = 12 s in (5 t - 4 x)$
Comparing in $y = A s in (wt - k x)$
We have $A = 12, w = 5 an d k = 4$
$(wt - k x) =$ phase difference $= \frac{π}{2}$

$∴ ∣ 5 t - 4 x ∣ = \frac{π}{2}$
When $t = 0, 4 x = \frac{π}{2}$
$∴ x = \frac{π}{8} c m$

Q. A progressive wave is represented by y=12sin(5t−4x) cm . On this wave, how far away are the two points having a phase difference of 90∘ ?

2π​cm

4π​cm

8π​cm

16π​cm