Question 423: Waves

Question

A sound wave of frequency $$160 \mathrm{~Hz}$$ has a velocity of $$320 \mathrm{~m} / \mathrm{s}$$. When it travels through air, the particles having a phase difference of $$90^{\circ}$$, are separated by a distance of

Accepted Answer

$$\begin{aligned}
& \mathrm{f}=160 \mathrm{~Hz}, \mathrm{v}=320 \mathrm{~m} / \mathrm{s} \
& \lambda=\frac{\mathrm{v}}{\mathrm{f}}=\frac{320}{160}=2 \mathrm{~m}=200 \mathrm{~cm}
\end{aligned}$$
Phase difference $$\phi=\frac{2 \pi x}{\lambda}$$
$$\begin{aligned}
	herefore \quad \mathrm{x} & =\frac{\phi \lambda}{2 \pi} \
& =\frac{\pi}{2} \cdot \frac{\lambda}{2 \pi} \quad\left[\because \phi=\frac{\pi}{2}ight] \
& =\frac{\lambda}{4}=\frac{200}{4}=50 \mathrm{~cm}
\end{aligned}$$

Answer

50 cm

Answer

1 cm

Answer

25 cm

Answer

75 cm

Waves

A sound wave of frequency $160 \mathrm{~Hz} has a velocity of 320 \mathrm{~m} / \mathrm{s}. When it travels through air, the particles having a phase difference of 90^{\circ}$, are separated by a distance of

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