An ambulance is moving towards a stationary listener at a constant speed of 30 m.s⁻¹ - NSC Physical Sciences - Question 6 - 2016 - Paper 1

To calculate the frequency, we use the formula:

$f_s = \frac{v}{\lambda}$

Given:

• Speed of sound, $v = 340 \text{ m.s}^{-1}$
• Wavelength, $\lambda = 0.28 \text{ m}$

Substituting the values:

$f_s = \frac{340}{0.28} \approx 1214.29 \text{ Hz}$

For the listener, we apply the Doppler effect formula:

$f_l = f_s \frac{v + v_o}{v - v_s}$

Where:

• $f_l$ = frequency heard by the listener
• $v_s = 30 \text{ m.s}^{-1}$ (speed of ambulance, source)
• $v_o = 0 \text{ m.s}^{-1}$ (listener is stationary)
• $f_s \approx 1214.29 \text{ Hz}$
• $v = 340 \text{ m.s}^{-1}$

Substituting the values:

$f_l = 1214.29 \left( \frac{340 + 0}{340 - 30} \right)$

Calculating:

$f_l \approx 1214.29 \left( \frac{340}{310} \right) \approx 1276.83 \text{ Hz}$

DECREASES

When a star moves away, the spectral lines observed are shifted towards lower frequencies (redshift). This occurs because the wavelengths of light are stretched as the star moves away, resulting in longer wavelengths and lower energy. By analyzing the spectral lines of a distant star, if they are observed to be redshifted, we can conclude that the star is receding from the Earth.