A Level Physics Practice Exam

What is the minimum distance between two points in water that are π/3 rad out of phase if the frequency is 2500 Hz?

1. 0.05 m

2. 0.1 m

3. 0.15 m

4. 0.2 m

The correct answer is: 0.1 m

To find the minimum distance between two points in water that are π/3 radians out of phase at a frequency of 2500 Hz, we start by determining the wavelength of the wave in water. The speed of sound in water is approximately 1500 m/s. The relationship between speed (v), frequency (f), and wavelength (λ) is given by the equation: \[ v = f \cdot \lambda \] Rearranging this formula allows us to find the wavelength: \[ \lambda = \frac{v}{f} = \frac{1500 \, \text{m/s}}{2500 \, \text{Hz}} = 0.6 \, \text{m} \] Next, to find the minimum distance between two points that are π/3 radians out of phase, we relate the phase difference to the distance. The phase difference, in radians, can be expressed in terms of the wavelength as follows: \[ \text{Phase Difference} = \frac{2\pi}{\lambda} \cdot d \] Where \( d \) is the distance. For a phase difference of π/3 radians, we set up the equation: \[ \frac{2\