Question

An ambulance is driving towards the hospital at a velocity 99.9 km/h and emitting a steady 786-Hz sound from its siren. The sound reflects off the front of the hospital and is received by the same ambulance. In addition to it's own siren, the ambulance hears a shifted tone from the reflection at what frequency? The speed of sound on this day is 343 m/s.

Answer 1

The frequency is 924.3 Hz.

Step-by-step explanation:

Given that,

Velocity of ambulance = 99.9 Km/h

Sound frequency = 786 Hz

We need to calculate the frequency

Using formula of frequency

`f=f_(0)((v+v_(0))/(v-v_(0)))`

Where, v = speed of sound

v₀ = velocity of observer

f₀ = Observer frequency

Put the value into the formula

`f=786*((343+99.9*(5)/(18))/(343-99.9*(5)/(18)))`

`f=924.3\ Hz`

Hence, The frequency is 924.3 Hz.

Answer 2

924.376 Hz

Step-by-step explanation:

Data provided in the question:

Velocity of the ambulance, v = 99.9 km/h =
`99.9 *(5)/(18)` m/s

= 27.75 m/s

Frequency of the sound, f₀ = 786 Hz

Speed of the sound, V = 343 m/s

Now,

Using the Doppler's effect formula, we have

Frequency heard =
`f_0*[(V+v)/(V-v)]`

Thus,

Frequency heard =
`786*[(343+27.75)/(343-27.75)]`

or

Frequency heard = 786 × 1.176

or

Frequency heard = 924.376 Hz