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. This is because the detected frequency of sound (437 Hz) is lower than the actual frequency emitted by the ship. According to the Doppler effect, a decrease in frequency indicates that the source is moving away from the observer.

To calculate the speed of the ship, we can use the formula for the Doppler effect:

$F_L = F_S \frac{v + v_L}{v + v_S}$

Where:

• $F_L$ = observed frequency (437 Hz)
• $F_S$ = actual frequency (calculated as $F_L / 0.985$)
• $v$ = speed of sound in water (1470 m/s)
• $v_L$ = speed of the listener (0 m/s, since the submarine is at rest)
• $v_S$ = speed of the source (the ship, which we need to calculate)

1. Calculate the actual frequency: $F_S = \frac{F_L}{0.985} = \frac{437}{0.985} \approx 443.65 \text{ Hz}$

2. Now we can rearrange the formula to find the speed of the source: $F_L = F_S \frac{v}{v + v_S}$ Rearranging gives us: $F_L (v + v_S) = F_S v$ $F_L v + F_L v_S = F_S v$ $F_L v_S = F_S v - F_L v$ $v_S = \frac{(F_S - F_L)v}{F_L}$ Plugging in the values: $v_S = \frac{(443.65 - 437) \times 1470}{437} \approx 22.39 \text{ m/s}$

The red shift phenomenon occurs when light from distant galaxies is stretched to longer wavelengths as they move away from us. This stretching indicates that the universe is expanding. By measuring the red shift of light from galaxies, astronomers can determine how fast those galaxies are receding. The greater the red shift, the faster the galaxy is moving away, which supports the theory that the universe is expanding over time.

The spectrum of the other galaxy constitutes a RED SHIFT. If absorption lines in the spectrum are moved towards the red end, it indicates that the galaxy is moving away from us, thus demonstrating a red shift.