A police car is travelling at a constant speed of 31.0 m s⁻¹ towards a stationary observer - Scottish Highers Physics - Question 9 - 2022

To find the frequency of the sound heard by the observer, we use the Doppler effect formula for a source moving towards a stationary observer:

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

Where:

• $f'$ is the observed frequency
• $f$ is the source frequency (820 Hz)
• $v$ is the speed of sound in air (340 m/s)
• $v_o$ is the speed of the observer (0 m/s, as the observer is stationary)
• $v_s$ is the speed of the source (31.0 m/s)

Substituting the values into the formula:

$f' = 820 \frac{340 + 0}{340 - 31}$

Calculating the denominator: $v - v_s = 340 - 31 = 309 \, \text{m/s}$

Now, substituting this back into the formula gives:

$f' = 820 \frac{340}{309}$

Calculating the multiplication: $f' = 820 \times 1.0990 \approx 901.6 \text{ Hz}$

Rounding this value gives approximately 902 Hz. Therefore, the answer is:

E 902 Hz.