An ambulance siren emits sound of frequency 400 Hz and the ambulance drives at 20 m/s straight towards a listener who is standing still. Taking the speed of sound as 340 m/s, what frequency does the listener hear?

1. Use the Doppler relation for a moving source and a stationary listener. 2. The observed frequency equals the emitted frequency multiplied by the speed of sound divided by the speed of sound minus the speed of the source. 3. The listener is not moving, so the numerator is simply the speed of sound, 340 metres per second. 4. The source moves towards the listener, so the speed of the source is subtracted in the denominator. 5. The denominator is 340 minus 20, which is 320 metres per second. 6. So the heard frequency is 400 hertz multiplied by 340 divided by 320. 7. Three hundred and forty divided by 320 is 1.0625, and 400 multiplied by 1.0625 is 425 hertz. 8. The 378 hertz answer traps anyone who adds the speed of the source in the denominator, which is the case for an ambulance driving away, while 400 hertz assumes no shift at all and 450 hertz rounds the ratio up to 1.125 by mistake. _Source: Siyavula Physical Sciences Grade 12 (Everything Science, CC BY 4.0), Chapter 6: Doppler effect_