A racing car moving towards a cliff sounds its horn. driver observes that sound reflected from cliff

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14.Waves and Sound

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A racing car moving towards a cliff sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If $v$ is the velocity of sound, the velocity of the car will be

$\frac{v}{{\sqrt 2 }}$

$\frac{v}{2}$

$\frac{v}{3}$

$\frac{v}{4}$

Solution

Octave = twice

$2 \mathrm{f}=\mathrm{f}_{0}\left(\frac{\mathrm{v}}{\mathrm{v}-\mathrm{v}_{\mathrm{s}}}\right) \cdot\left(\frac{\mathrm{v}+\mathrm{v}_{0}}{\mathrm{v}}\right)$

$2 \mathrm{f}=\mathrm{f}\left(\frac{\mathrm{v}+\mathrm{v}_{0}}{\mathrm{v}-\mathrm{v}_{\mathrm{s}}}\right) \quad\left(\mathrm{v}_{\mathrm{s}}=\mathrm{v}_{0}\right)$

$2\left(\mathrm{v}-\mathrm{v}_{\mathrm{c}}\right)=\mathrm{v}+\mathrm{v}_{\mathrm{c}}$

$3 \mathrm{v}_{\mathrm{c}}=\mathrm{v}$

$v_{c}=\frac{v}{3}$

Standard 11

Physics

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A racing car moving towards a cliff sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If $v$ is the velocity of sound, the velocity of the car will be

Solution

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The equation of a stationary wave is

$y = 0.8\,\cos \,\,\left( {\frac{{\pi x}}{{20}}} \right)\,\sin \,200\,\pi t$

where $x$ is in $cm$ and $t$ is in $sec$ . The separtion between consecutive nodes will be …. $cm$