The pitch of a musical note depends on its frequency - Leaving Cert Physics - Question b - 2008

The loudness of a musical note is influenced by the following factors:

1. Amplitude: The amplitude of the sound wave directly affects loudness; greater amplitudes produce louder sounds.

2. Intensity: Loudness is also related to the intensity of the sound wave, which is the power per unit area carried by the wave. If more acoustic energy enters the ear, the perceived loudness increases.

3. Distance: The distance from the sound source plays a role. The farther away you are, the quieter the sound seems due to the spreading of sound waves.

The Doppler effect is the observed change in frequency or wavelength of a wave in relation to an observer moving relative to the wave source. It is caused by the relative motion between the source and the observer. If the source is moving towards the observer, the frequency appears higher (blue shift), and if it’s moving away, the frequency appears lower (red shift). This phenomenon is commonly observed with sound waves, light waves, and is widely used in various applications such as radar and astronomy.

To calculate the change in pitch observed as the car moves away, we use the Doppler effect formula:

$f' = f \frac{v + v_o}{v - v_s}$

Where:

• $f'$ is the observed frequency,
• $f$ is the source frequency (1520 Hz),
• $v$ is the speed of sound in air (approximately 340 m s⁻¹),
• $v_o$ is the speed of the observer (0 m s⁻¹, stationary observer),
• $v_s$ is the speed of the source (55 m s⁻¹).

1. Calculating the observed frequency as the source approaches: $f_{approaching} = 1520 \frac{340 + 0}{340 - 55} = 1520 \frac{340}{285} \approx 1813.33 \text{ Hz}$

2. Calculating the observed frequency as the source moves away: $f_{receding} = 1520 \frac{340 + 0}{340 + 55} = 1520 \frac{340}{395} \approx 1308.35 \text{ Hz}$

3. The change in pitch is given by: $\Delta f = f_{approaching} - f_{receding} \approx 1813.33 - 1308.35 = 504.98 \text{ Hz}$

Thus, the change in pitch observed as the car moves away is approximately 505 Hz.

One application of the Doppler effect is in the field of astronomy, where it is used to calculate the speeds of stars and galaxies. By analyzing the shift in the light spectrum (redshift for objects moving away and blueshift for objects moving closer), astronomers can determine the velocity at which these celestial bodies are moving. This technique provides valuable information about the expansion of the universe and the motion of objects in space.