Question

8. What is the frequency heard by a person driving at 15.0 m/s toward a blowing factory whistle (800. Hz) if the speed of sound is 340.6 m/s? (837 Hz) F= (340.6×800)÷(340.6-15)= 836.9 Hz F=836.9 9. From the previous problem, what frequency would he hear after passing the factory if he continues at the same speed? (766 Hz)

Answer 1

The frequency heard by a person driving towards a factory whistle emitting an 800 Hz tone is approximately 837 Hz. After passing the factory and moving away, the frequency heard is approximately 766 Hz. These calculations are based on the Doppler effect equation.

Step-by-step explanation:

Doppler Effect Calculation

The frequency heard by a person driving at 15.0 m/s toward a blowing factory whistle initially at 800 Hz can be calculated using the Doppler effect. The formula to find the observed frequency (f') when moving towards the source is:

f' = (v + vo) / (v - vs) * fs

where:

v is the speed of sound (340.6 m/s in this case),

vo is the speed of the observer (15.0 m/s towards the source),

vs is the speed of the source (0 m/s, as the whistle is stationary), and

fs is the frequency of the source (800 Hz).

Therefore, the observed frequency is: f' = (340.6 + 15.0) / (340.6 - 0) * 800 = 837 Hz, approximately.

After passing the factory and moving away, the observed frequency can be calculated using the formula with the observer's speed as a negative (since they're moving away from the source):

f' = (v - vo) / (v + vs) * fs

The observed frequency when moving away is: f' = (340.6 - 15.0) / (340.6 + 0) * 800 = 766 Hz, approximately.

Answer 2

A) f_o ≈ 836.9 Hz

B) f ≈ 765 Hz

Step-by-step explanation:

A) To solve this, we will use the formula;

f_o = (v•f_s)/(v - v_p)

Where;

v is speed of sound in air

f_s is frequency of source

v_p is the speed of the person moving towards the whistle.

We are given;

v = 340.6 m/s

v_p = 15 m/s

f_s = 800 Hz

Thus;

f_o = (340.6 × 800)/(340.6 - 15)

f_o ≈ 836.9 Hz

B) to solve this, let's first calculate the wavelength from the formula;

λ = v/f_s

λ = 340.6/800

λ = 0.42575 m

To get the frequency he will hear after passing the factory, we will use the formula;

f = (v - v_p)/λ

f = (340.6 - 15)/0.42575

f ≈ 765 Hz