Two trains $$A$$ and $$B$$ are moving with speeds $$20 \mathrm{~m} / \mathrm{s}$$ and $$30 \mathrm{~m} / \mathrm{s}$$ respectively in the same direction on the same straight track, with $$B$$ ahead of $$A$$. The engines are at the front ends. The engines of train A blows a long whistle.
Assume that the sound of the whistle is composed of components varying in frequency from $$f_{1}=800 \mathrm{~Hz}$$ to $$f_{2}=1120 \mathrm{~Hz}$$, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus $$320 \mathrm{~Hz}$$. The speed of sound in still air is $$340 \mathrm{~m} / \mathrm{s}$$.
The spread of frequency as observed by the passengers in train B is
The figure shows surface XY separating two transparent media, medium -1 and medium -2 . The lines ab and cd represent wavefronts of a light wave traveling in medium -1 and incident on X Y. The lines ef and gh represent wavefronts of the light wave in medium -2 after refraction.
Light travels as a
The figure shows surface XY separating two transparent media, medium -1 and medium -2 . The lines ab and cd represent wavefronts of a light wave traveling in medium -1 and incident on X Y. The lines ef and gh represent wavefronts of the light wave in medium -2 after refraction.
The phases of the light wave at $$c, d, e$$ and $$f$$ are $$\phi_c, \phi_d, \phi_{e}$$ and $$\phi_{f}$$ respectively.
It is given that $$\phi_{c} \neq \phi_{f}$$.
The figure shows surface XY separating two transparent media, medium -1 and medium -2 . The lines ab and cd represent wavefronts of a light wave traveling in medium -1 and incident on X Y. The lines ef and gh represent wavefronts of the light wave in medium -2 after refraction.
Speed of the light is