11. ⇒ (MHT CET 2021 21th September Morning Shift )

A simple harmonic progressive wave is given by $Y = Y_{0} \sin 2 π (n t - \frac{x}{λ})$ . If the wave velocity is ${(\frac{1}{8})}^{th}$ the maximum particle velocity then the wavelength is

A. $\frac{π Y_{0}}{2}$

B. $\frac{π Y_{0}}{4}$

C. $\frac{π Y_{0}}{8}$

D. $\frac{π Y_{0}}{16}$

Correct Option is (B)

Maximum particle velocity $= Y_{0} ω = 2 π n Y_{0}$

Wave velocity $= n λ$

$\begin{aligned} ∴ \frac{2 π n Y_{0}}{8} = n λ \\ ∴ λ = \frac{π Y_{0}}{4} \end{aligned}$

12. ⇒ (MHT CET 2021 20th September Morning Shift )

The equation of wave is given by $y = 10 \sin (\frac{2 π t}{30} + α)$ . If the displacement is $5 cm$ at $t = 0$ , then the total phase at $t = 7.5 s$ will be

$[\sin 30^{\circ} = \cos 60^{\circ} = \frac{1}{2}, \cos 30^{\circ} = \sin 60^{\circ} = \frac{\sqrt{3}}{2}]$

A. $\frac{π}{3} rad$

B. $\frac{π}{2} rad$

C. $\frac{2 π}{5} rad$

D. $\frac{2 π}{3} rad$

Correct Option is (D)

$\begin{aligned} y = 10 \sin (\frac{2 π t}{30} + α) \\ At t = 0, y = 5 cm ∴ 5 = 10 \sin α \\ ∴ \sin α = \frac{1}{2} ∴ α = \frac{π^{c}}{6} \\ At t = 7.5, the total phase \\ ϕ = \frac{2 π \times 7.5}{30} + α \\ = \frac{π}{2} + α \\ = \frac{π}{2} + \frac{π}{6} = \frac{2 π}{3} rad \end{aligned}$

13. ⇒ (MHT CET 2021 20th September Morning Shift )

The frequency of a tuning fork is 'n' Hz and velocity of sound in air is 'V' m/s. When the tuning fork completes 'x' vibrations, the distance travelled by the wave is

A. $\frac{V}{xn}$

B. $\frac{Vn}{x}$

C. $\frac{xV}{n}$

D. $\frac{x}{Vn}$

Correct Option is (C)

Period $= \frac{1}{n}$

Time required for x vibrations, $t = \frac{x}{n}$

Distance travelled by the wave, $Vt = \frac{xV}{n}$

⇒Superposition of Waves