A train, standing at the outer signal of a railway station blows a whistle of frequency 400 \mathrm{~Hz} in still air. (i) What is the frequency of the whistle for a platform observer when the train (a) approaches the platform with a speed of 10 \mathrm{~m} \mathrm{~s}^{-1}, (b) recedes from the platform with a speed of 10 \mathrm{~m} \mathrm{~s}^{-1} ? (ii) What is the speed of sound in each case? The speed of sound in still air can be taken as \mathbf{3 4 0} \mathrm{m} \mathrm{s}^{-1}.
A train, standing at the outer signal of a railway station blows a whistle of frequency 400 \mathrm{~Hz} in still air. (i) What is the frequency of the whistle for a platform observer when the train (a) approaches the platform with a speed of 10 \mathrm{~m} \mathrm{~s}^{-1}, (b) recedes from the platform with a speed of 10 \mathrm{~m} \mathrm{~s}^{-1} ? (ii) What is the speed of sound in each case? The speed of sound in still air can be taken as \mathbf{3 4 0} \mathrm{m} \mathrm{s}^{-1}.

Frequency of the whistle is given as =400 \mathrm{~Hz}

Speed of sound in still air is given as =340 \mathrm{~m} / \mathrm{s}

(i)

(a)Train approaches the platform at a speed given as \mathrm{v}_{\mathrm{s}}=10 \mathrm{~m} / \mathrm{s}

Frequency of the whistle for a platform observer can be calculated as,

f^{\prime}=\frac{v}{v-v_{s}} \times f

f^{\prime}=\frac{340}{340-10} \times 400=412 \mathrm{~Hz}

(b) Train recedes from the platform at a speed given as,
\mathrm{v}_{\mathrm{s}}=10 \mathrm{~m} / \mathrm{s}

Frequency of the whistle for a platform observer can be calculated as,

f^{\prime}=\frac{v}{v+v_{s}} \times f

f^{\prime}=\frac{340}{340+10} \times 400=389 \mathrm{~Hz}

(ii) The speed of the sound will not change, that is 340 \mathrm{~m} / \mathrm{s}.