Doppler Effect

The Doppler effect for sound in NCERT Class 11, Chapter 15 (Waves) gives the apparent frequency when a source moves toward a stationary observer as $f^{\prime }=f\left(\frac{v}{v-v_s}\right)$, where $v$ is the speed of sound and $v_s$ is the source speed. With $f=400$ Hz, $v=340$ m/s and $v_s=30$ m/s, the denominator is $340-30=310$ m/s, so $f^{\prime }=400\times \frac{340}{310}=400\times 1.097\approx 439$ Hz. The frequency rises because the approaching source crowds the wavefronts together. The option 365 Hz uses $v+v_s$ in the denominator, which applies to a receding source and wrongly lowers the pitch. The option 400 Hz ignores the motion entirely. The option 470 Hz overestimates by using too small a denominator, such as $340-60$. It is important to distinguish moving-source from moving-observer situations: here the source moves, so the correction appears in the denominator through $v-v_s$, whereas a moving observer would place the correction in the numerator instead, and the two formulas give slightly different results even for equal speeds. As the ambulance passes and begins to recede, the perceived frequency would abruptly drop to $400\times 340/(340+30)\approx 367$ Hz, producing the familiar falling pitch heard after a vehicle goes by. A plausibility check: an approaching siren should sound higher-pitched, and a rise from 400 to about 439 Hz, roughly a 10% increase for a source at nearly a tenth of the sound speed, is physically reasonable in both direction and magnitude.