Question 217: Waves

Question

Two tuning forks when sounded together produce 4 beats per second. One of the forks is in unison with 23 cm length of sonometer wire and other with 24 cm length of the same wire. The frequencies of the two tuning forks are

Accepted Answer

Given number of beats $=4, l_1=0.23 \mathrm{~m}$, $l_2=0.24 \mathrm{~m}$
The frequencies of the given sonometer are ${ }^{a s}$ follows:
$$ \begin{aligned} & \mathrm{f}_1=\frac{1}{2 l_1} \sqrt{\frac{\mathrm{~T}}{\mathrm{~m}}} \ & \mathrm{f}_2=\frac{1}{2 l_2} \sqrt{\frac{\mathrm{~T}}{\mathrm{~m}}} \end{aligned} $$
$$ \begin{aligned} & f_1-f_2=4 \ & \frac{1}{2 l_1} \sqrt{\frac{T}{m}}-\frac{1}{2 l_2} \sqrt{\frac{T}{m}}=4 \ & \left(\frac{1}{2(0.23)}-\frac{1}{2(0.24)}ight) \sqrt{\frac{T}{m}}=4 \ & \sqrt{\frac{T}{m}}=44.16 \ &	herefore f_1=96 \mathrm{~Hz} 	ext { and } f_2=92 \mathrm{~Hz} \end{aligned} $$

Answer

$96 \mathrm{~Hz}, 92 \mathrm{~Hz}$

Answer

$92 \mathrm{~Hz}, 88 \mathrm{~Hz}$

Answer

$72 \mathrm{~Hz}, 68 \mathrm{~Hz}$

Answer

$48 \mathrm{~Hz}, 44 \mathrm{~Hz}$

Waves

Two tuning forks when sounded together produce 4 beats per second. One of the forks is in unison with 23 cm length of sonometer wire and other with 24 cm length of the same wire. The frequencies of the two tuning forks are

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