Waves

JEE Main level, single correct, medium

117 of 142

Question 117 of 142

The velocity of sound in a gas, in which two wavelengths 4.08m4.08m and 4.16m4.16m produce 4040 beats in 12s12s, will be

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Answer: (D) 707.2ms−1707.2m{s}^{-1}

If the velocity of the sound in the medium is vv then, f1=v4.08{f}_{1}=\dfrac{v}{4.08} and f2=v4.16{f}_{2}=\dfrac{v}{4.16}
Now beat frequency,

fb=Δf=∣f1−f2∣=4012=103Hz⇒v[14.08−14.16]=103Hz⇒707.2ms−1{f}_{b}=\Delta f=\left|{f}_{1}-{f}_{2}\right|=\dfrac{40}{12}=\dfrac{10}{3}Hz \Rightarrow v\left[\dfrac{1}{4.08}-\dfrac{1}{4.16}\right]=\dfrac{10}{3}Hz\Rightarrow 707.2m{s}^{-1}

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