An ambhulance blowing a siren of frequency 700Hz is travelling slowly towards vertical reflectoing wall with a speed 2m/s. The speed of sound is 350m/s. How many beats ar heard per sec to the driver of het ambluance?

Sure, let's solve this step by step:

1. First, we need to calculate the frequency of the sound that the ambulance driver hears directly from the siren. This can be done using the Doppler effect formula for frequency:

   f' = f * (v + vd) / v

   where: f' is the observed frequency, f is the source frequency, v is the speed of sound, vd is the speed of the observer (ambulance driver in this case).

   Substituting the given values:

   f' = 700 * (350 + 2) / 350 = 704 Hz

2. Next, we need to calculate the frequency of the sound that the ambulance driver hears after it reflects off the wall. This is a two-step process because the sound wave first travels to the wall and then reflects back to the ambulance. We use the Doppler effect formula for frequency twice:

   f'' = f * (v + vr) / (v - vs)

   where: f'' is the observed frequency after reflection, vr is the speed of the reflector (wall in this case, which is stationary, so vr = 0), vs is the speed of the source (ambulance in this case).

   Substituting the given values for the first step (sound traveling to the wall):

   f1 = 700 * (350 + 0) / (350 - 2) = 706.04 Hz

   For the second step (sound reflecting back to the ambulance), the ambulance is now the observer and the wall is the source. So, we use the first Doppler effect formula again:

   f'' = f1 * (v + vd) / v = 706.04 * (350 + 2) / 350 = 710.14 Hz

3. Finally, the beat frequency is the absolute difference between the two frequencies:

   Beat frequency = |f'' - f'| = |710.14 - 704| = 6.14 Hz

So, the driver of the ambulance hears approximately 6 beats per second.