Question 375: Waves

Question

Two sounding sources send waves at certain temperature in air of wavelength $$50 \mathrm{~cm}$$ and $$50.5 \mathrm{~cm}$$ respectively. The frequency of sources differ by $$6 \mathrm{~Hz}$$. The velocity of sound in air at same temperature is

Accepted Answer

$$\mathrm{v}=\mathrm{n} \lambda$$
Since, both the sound sources are at same temperature, velocity of sound in both cases would be the same.
$$\begin{array}{ll}
	herefore \quad & \mathrm{v}=\left(50 \mathrm{n}_1ight) \mathrm{cm} / \mathrm{s} \quad 	ext{.... (i)}\
& \mathrm{v}=\left(50.5 \mathrm{n}_2ight) \mathrm{cm} / \mathrm{s} \quad 	ext{.... (ii)}\
& \frac{\mathrm{n}_1}{\mathrm{n}_2}=\frac{50.5}{50} \quad 	ext{...[From (i) and (ii)]} \
	herefore \quad & \frac{\mathrm{n}_1-\mathrm{n}_2}{\mathrm{n}_2}=\frac{50.5-50}{50}
\end{array}$$
$$\begin{array}{ll}
	herefore & \frac{6}{\mathrm{n}_2}=\frac{0.50}{50}=\frac{1}{100} \quad \ldots .\left(\because \mathrm{n}_1-\mathrm{n}_2=6 \mathrm{~Hz}ight) \
	herefore & \mathrm{n}_2=600 \mathrm{~Hz} \
	herefore & \mathrm{v}=\frac{50.5 	imes 600}{100} \mathrm{~m} / \mathrm{s} \quad \ldots .[	ext { From (ii) }] \
	herefore & \mathrm{v}=303 \mathrm{~m} / \mathrm{s}
\end{array}$$

Answer

$$300 \mathrm{~m} / \mathrm{s}$$

Answer

$$303 \mathrm{~m} / \mathrm{s}$$

Answer

$$313 \mathrm{~m} / \mathrm{s}$$

Answer

$$330 \mathrm{~m} / \mathrm{s}$$

Waves

Two sounding sources send waves at certain temperature in air of wavelength $50 \mathrm{~cm} and 50.5 \mathrm{~cm} respectively. The frequency of sources differ by 6 \mathrm{~Hz}$. The velocity of sound in air at same temperature is

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