Question

You are driving down the road heading north at 15 m/s. An ambulance is driving in the opposite direction (south) towards you at 25 m/s. If the ambulance's siren emits sound at a frequency of 2 kHz, what frequency do you hear? Assume that the speed of sound is 340 m/s. a. 1780 Hz b. 1945 Hz c. 2254 Hz d. 2063 Hz e. 2000 Hz

Answer 1

Answer:

d. 2063 Hz

Explanation:

Given that the source of the sound (the ambulance) is heading towards the observer, we have;

fL= (v ± vL/v ± vS) fS

Where;

v = speed of sound = 340 m/s

vL = velocity of the listener = 15 m/s

vS = velocity of the source = 25 m/s

fS = frequency of source = 2 kHz

Since the source is moving towards the observer we subtract;

Substituting values;

fL = (340 - 15/340 - 25)2 *10^3

fL = 2063Hz

Answer 2

The frequency of the siren heard by the driver is approximately 2254Hz.

Hence, Option C) 2254Hz is the correct answer.

Given the data in the question;

• Velocity of observer; $v_o = 15m/s$

• Velocity of source; $v_s = 25m/s$

• Actual frequency (source); $f = 2kHz = 2000Hz$

• Velocity of sound; $v = 340m/s$

Frequency heard by observer; $f' = \ ?$

To find the frequency heard by the observer, we Doppler Effect Equation:

$f' = [ \frac{v+v_o}{v - v_s} ] f$

Where $f'$ is the observed frequency, $f$ is the actual frequency, $v$ is the velocity of sound, $v_o$ is the velocity of the observer and $v_s$ is the velocity of the source.

We substitute our given values into the equation

$f' = [ \frac{340m/s\ +\ 15m/s}{340m/s\ -\ 25m/s} ] 2000Hz\\\\f' = [ \frac{355m/s}{315m/s} ] 2000Hz\\\\f' = 2253.968Hz\\\\f' = 2254Hz$

The frequency of the siren heard by the driver is approximately 2254Hz.

Hence, Option C) 2254Hz is the correct answer.

Learn more: https://brainly.com/question/1330077