5.1 A submarine can use the Doppler effect to detect the speed of the ship - NSC Physical Sciences - Question 5 - 2016 - Paper 1

The ship is moving away from the submarine because the detected frequency of sound (437 Hz) is lower than the actual frequency of the sound emitted by the ship.

To find the speed of the ship, we can use the formula:
$f_L = f_S \left( \frac{v + v_0}{v - v_s} \right)$
Where:

• $f_L$ = observed frequency (437 Hz)
• $f_S$ = source frequency (0.985 times the frequency)
• $v$ = speed of sound in water (1470 m/s)
• $v_0$ = speed of observer (0, at rest)
• $v_s$ = speed of source (ship)

Using the values, the equation becomes:
$f_L = 0.985 f_S \left( \frac{v}{v - v_s} \right)$
Substituting the known values into the formula:

1. First, find the source frequency:
   $f_S = \frac{437}{0.985} \approx 443.65\text{ Hz}$
2. Next, substitute back into the Doppler equation to find the speed of the ship: $437 = 443.65 \left( \frac{1470}{1470 - v_s} \right)$
3. Rearranging gives us:
   $1470 - v_s = \frac{443.65 \cdot 1470}{437}$
4. Solving for $v_s$ results in:
   $v_s \approx 22.39 \text{ m/s}$
   Thus, the speed of the ship is approximately 22.39 m/s.

The phenomenon of red shift occurs when light from distant stars shows a shift towards the lower frequencies (or red end) of the spectrum. This is interpreted as an indication that the object is moving away from the observer, which is consistent with the observations that distant galaxies are receding from us. The further a galaxy is, the faster it appears to be moving away, which supports the Big Bang theory and the notion of an expanding universe.

The spectrum of the other galaxy constitutes a RED SHIFT since the absorption lines are shifted towards the red end of the spectrum compared to the spectrum from the Sun.