# Cosmology for SQA Higher Physics

1. The Doppler effect

The Doppler effect is the change in frequency due to the relative motion between the wave source and the observer. When both the observer and the source are stationary, the waves are at the same frequency for both. When the source moves towards the observer, the wavelength becomes shorter, and therefore the wave that is received by the observer has higher frequency, and vice versa when the source is moved away. An example of this is the fact that when an ambulance moves away from the observer with its siren blaring, the siren will sound lower in pitch as it moves away from the observer.

# 1

An ambulance is travelling at 30 m/s towards an observer. The frequency of the siren of the ambulance is 500 Hz. Given that the speed of sound is 340 m/s, calculate the frequency of the siren that the observer hears.

f = 500 × 340/(340 − 30) = 548 Hz (to 3 significant figures).

# 2

Define the Doppler effect.

The Doppler effect is the change in frequency due to the relative motion between the wave source and the observer.

# 3

A police car is travelling away from an observer. Explain how the observer will hear the siren.

When a police car moves away from the observer with its siren blaring, the siren will sound lower in pitch as it moves away from the observer.

# 4

Calculate the velocity of the ambulance in the given diagram. Use the fact that the speed of sound is 340 m/s.

400 = 520 × 340/(340 − v), so v = −28.3 m/s (to 3 significant figures). Therefore , the ambulance is travelling away from the observer.

# 5

A police car is travelling at 40 m/s towards an observer. The frequency of the siren of the car is 420 Hz. Given that the speed of sound is 340 m/s, calculate the frequency of the siren that the observer hears.

f = 420 × 340/(340 − 40) = 476 Hz.

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