Question

A factory whistle blows at a frequency of 1216 HZ. What pitch will the passengers of a car moving at 28 m/s away from the whistle hear if the speed of sound is 343 m/s.1) 1315 Hz2) 1324 Hz3) 1188 Hz4) 1117 Hz

Answer 1

The pitch heard by the passengers of the car will be about 1317 Hz.

Step-by-step explanation:

The pitch heard by the passengers of a car moving away from a factory whistle can be calculated using the Doppler effect equation:

f' = f * (v + v_obs)/(v + v_source)

Where:

• f' is the observed frequency
• f is the source frequency (1216 Hz)
• v is the speed of sound (343 m/s)
• v_obs is the speed of the observer (28 m/s)
• v_source is the speed of the source (0 m/s)

Plugging in the values:

f' = 1216 * (343 + 28)/(343 + 0)

f' = 1216 * (371/343)

f' = 1317 Hz (approximately)

Therefore, the passengers of the car will hear a pitch of about 1317 Hz.

Answer 2

Given,

The frequency of the source, f=1216 Hz

The speed with which the car is moving away from the source, v₀=28 m/s

The speed of the sound, v=343 m/s

The frequency with which the observer hears the sound is given by,

`f_0=(v-v_0)/(v)f`

On substituting the known values,

`\begin{gathered} f_0=(343-28)/(343)*1216 \\ =1116.7\text{ Hz} \\ \approx1117\text{ Hz} \end{gathered}`

Thus the frequency heard by the observer is 1117 Hz. Therefore the correct answer is option 4.