What is meant by the Doppler effect? (apparent) change in frequency of a wave due to (relative) motion between source and observer Define centripetal force - Leaving Cert Physics - Question c - 2016

Centripetal force is the force that acts on an object moving in a circular path, directed towards the center of the circle. It is necessary for maintaining the object's circular motion.

To find the maximum and minimum frequency detected by the observer, we can use the Doppler effect formulas for a moving source. Given:

• Frequency of the source, $f = 1.1 ext{ kHz} = 1100 ext{ Hz}$
• Speed of sound in air, $v = 340 ext{ m/s}$
• Speed of the source, $u = 13 ext{ m/s}$

The maximum frequency when the source is moving towards the observer is given by:

$f_{max} = f \left(\frac{v + u}{v - 0}\right) = 1100 \left(\frac{340 + 13}{340}\right) \approx 1143.7 \text{ Hz}$

The minimum frequency when the source is moving away from the observer is:

$f_{min} = f \left(\frac{v - u}{v - 0}\right) = 1100 \left(\frac{340 - 13}{340}\right) \approx 1059.5 \text{ Hz}$

To determine the maximum and minimum tension in the string, we use these formulas:

1. Maximum Tension when the buzzer is at the bottom of the circle:

$T_{max} = \frac{mv^2}{r} + mg$

Where:

• $m = 0.07 ext{ kg}$ (mass of the buzzer)
• $v = 13 ext{ m/s}$ (speed of the buzzer)
• $r = 0.8 ext{ m}$ (radius)
• $g = 9.8 ext{ m/s}^2$ (acceleration due to gravity)

Calculating:

$T_{max} = \frac{0.07 \cdot (13)^2}{0.8} + (0.07 \cdot 9.8) \approx 15.5 ext{ N}$

2. Minimum Tension when the buzzer is at the top of the circle:

$T_{min} = \frac{mv^2}{r} - mg$

Calculating:

$T_{min} = \frac{0.07 \cdot (13)^2}{0.8} - (0.07 \cdot 9.8) \approx 14.1 ext{ N}$