The Doppler effect is the apparent change in the frequency or wavelength of a wave (like sound or light) due to the relative motion between the source of the wave and the observer.

The Doppler effect formula for a moving listener approaching a stationary source is:

$$f_L = f_s \left( \frac{v + v_L}{v} \right)$$

Given:

• Source frequency $f_s = 170 \text{ Hz}$
• Speed of sound $v = 340 \text{ m}\cdot\text{s}^{-1}$
• Listener speed $v_L = 12 \text{ m}\cdot\text{s}^{-1}$

$$x = 170 \text{ Hz} \left( \frac{340 \text{ m}\cdot\text{s}^{-1} + 12 \text{ m}\cdot\text{s}^{-1}}{340 \text{ m}\cdot\text{s}^{-1}} \right)$$ $$x = 170 \text{ Hz} \left( \frac{352}{340} \right)$$ $$x = 170 \text{ Hz} \times 1.03529$$ $$x \approx 176 \text{ Hz}$$

The observed frequency is still $x = 176 \text{ Hz}$.
The listener now travels towards the stationary sound source at $v_L = 24 \text{ m}\cdot\text{s}^{-1}$.
The formula is:

$$f_L = f_s' \left( \frac{v + v_L}{v} \right)$$

Rearrange to solve for $f_s'$:

$$f_s' = f_L \left( \frac{v}{v + v_L} \right)$$

Substitute the values:

$$f_s' = 176 \text{ Hz} \left( \frac{340 \text{ m}\cdot\text{s}^{-1}}{340 \text{ m}\cdot\text{s}^{-1} + 24 \text{ m}\cdot\text{s}^{-1}} \right)$$ $$f_s' = 176 \text{ Hz} \left( \frac{340}{364} \right)$$ $$f_s' = 176 \text{ Hz} \times 0.934065$$ $$f_s' \approx 164.395 \text{ Hz}$$

The new frequency of the sound source is $\boxed{\text{164.40 Hz}}$.

6.2

The spectrum that shows the absorption lines of light from another star that is moving AWAY from Earth is Z.

Explanation: When a star moves away from Earth, the light it emits undergoes redshift. This means the wavelengths of the absorption lines are shifted towards the red end of the spectrum (longer wavelengths). Compared to the reference spectrum X (from the sun), spectrum Z shows the absorption lines shifted towards the 'R' (red) side, indicating redshift.