A Level Physics Practice Exam

If the least distance between two points of a wave with a phase difference of π/3 radians is 0.050 m, what is the speed of the wave if its frequency is 500 Hz?

1. 75 m/s

2. 100 m/s

3. 150 m/s

4. 200 m/s

The correct answer is: 150 m/s

To solve this question, we start with the concept of phase difference and wave speed. The phase difference \( \Delta \phi \) between two points on a wave is related to the distance \( \Delta x \) between them and the wavelength \( \lambda \) through the following relationship: \[ \Delta \phi = \frac{2\pi}{\lambda} \Delta x \] In this case, the phase difference is given as \( \frac{\pi}{3} \) radians and the least distance between two points is \( 0.050 \) m. Plugging the values into the equation: \[ \frac{\pi}{3} = \frac{2\pi}{\lambda} \times 0.050 \] We can rearrange this to find the wavelength \( \lambda \): \[ \lambda = \frac{2\pi \times 0.050}{\frac{\pi}{3}} = 2 \times 0.050 \times 3 = 0.300 \text{ m} \] Now that we have the wavelength, we can calculate the speed \( v \) of the wave using the formula that relates speed, frequency, and