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Home » A man standing at a certain distance from an observer blows a horn of frequency in still air. (a) Find the horn’s frequency for the observer when the man (i) runs towards him at (ii) runs away from him at .(b) Find the speed of sound in both the cases.[Speed of sound in still air is
A man standing at a certain distance from an observer blows a horn of frequency 200 \mathrm{~Hz} in still air.
(a) Find the horn’s frequency for the observer when the man (i) runs towards him at 20 \mathrm{~m} / \mathrm{s} (ii) runs away from him at \mathbf{2 0} \mathrm{m} / \mathrm{s}.
(b) Find the speed of sound in both the cases.
[Speed of sound in still air is \mathbf{3 4 0 \mathrm { m } / \mathrm { s } \text { ] }}
CBSE | Class 11 | NCERT | Physics | Waves
A man standing at a certain distance from an observer blows a horn of frequency 200 \mathrm{~Hz} in still air.
(a) Find the horn’s frequency for the observer when the man (i) runs towards him at 20 \mathrm{~m} / \mathrm{s} (ii) runs away from him at \mathbf{2 0} \mathrm{m} / \mathrm{s}.
(b) Find the speed of sound in both the cases.
[Speed of sound in still air is \mathbf{3 4 0 \mathrm { m } / \mathrm { s } \text { ] }}

Frequency of the horn is given as \mathrm{v}_{\mathrm{H}}=200 \mathrm{~Hz}

Velocity of the man is given as \mathrm{v}_{\mathrm{T}}=20 \mathrm{~m} / \mathrm{s}

Velocity of sound is given as v=340 \mathrm{~m} / \mathrm{s}

(a) We know,

(i) The apparent frequency of the horn as the man approaches the observer is:

v^{\prime}=v_{H}\left[v /\left(v-v_{T}\right)\right]

=200[340 /(340-20)]

=212.5 \mathrm{~Hz}

(ii) The apparent frequency of the horn as the man runs away from the observer is:

v^{\prime \prime}=v_{\mathrm{H}}\left[v /\left(v+v_{T}\right)\right]

=200[340 /(340+20)]

=188.88 \mathrm{~Hz}

(b) In all circumstances, the speed of sound is 340 ms^{-1}. The relative motions of the observer and the source cause the apparent shift in frequency.

i

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