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

Answer:

924.376 Hz

Explanation:

Data provided in the question:

Velocity of the ambulance, v = 99.9 km/h = $99.9 \times\frac{5}{18}$ 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 = $f_0\times[\frac{V+v}{V-v}]$

Thus,

Frequency heard = $786\times[\frac{343+27.75}{343-27.75}]$

or

Frequency heard = 786 × 1.176

or

Frequency heard = 924.376 Hz

Answer 2

Answer:

The frequency is 924.3 Hz.

Explanation:

Given that,

Velocity of ambulance = 99.9 Km/h

Sound frequency = 786 Hz

We need to calculate the frequency

Using formula of frequency

$f=f_{0}(\dfrac{v+v_{0}}{v-v_{0}})$

Where, v = speed of sound

v₀ = velocity of observer

f₀ = Observer frequency

Put the value into the formula

$f=786\times(\dfrac{343+99.9\times\dfrac{5}{18}}{343-99.9\times\dfrac{5}{18}})$

$f=924.3\ Hz$

Hence, The frequency is 924.3 Hz.