Question 9: Waves

Question

The wavelength of two waves are 40 and $$42 \mathrm{~cm}$$ respectively. If the temperature of the room is $$20^{\circ} \mathrm{C}$$ then what will be the number of beats produced per second by these waves. When the speed of sound at $$0^{\circ} \mathrm{C}$$ is $$332 \mathrm{~m} / \mathrm{s}$$ ?

Accepted Answer

Beats will be formed as the wavelengths (hence frequencies) are similar.
$$\begin{aligned}
& \lambda_1=40 \mathrm{~cm} ~\lambda_2=42 \mathrm{~cm} \
& v \propto \sqrt{T} \
& \Rightarrow \quad \frac{v_1}{v_2}=\left(\frac{T_2}{T_1}ight)^{1 / 2}=\left(\frac{273+20}{273}ight) \
& \Rightarrow \quad v_2=319.23 \
& v_1=\frac{v_1}{\lambda_1}=\frac{319.23}{0.40}=798.075 \mathrm{~Hz} \
& v_2=\frac{v_2}{\lambda_2}=\frac{319.23}{0.42}=760.071 \mathrm{~Hz} .
\end{aligned}$$
No. of beats $$=v_2-v_1=798-760=38 \mathrm{~Hz}$$

Answer

34

Answer

38

Answer

44

Answer

None of these

Waves

The wavelength of two waves are 40 and $42 \mathrm{~cm} respectively. If the temperature of the room is 20^{\circ} \mathrm{C} then what will be the number of beats produced per second by these waves. When the speed of sound at 0^{\circ} \mathrm{C} is 332 \mathrm{~m} / \mathrm{s}$ ?

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