Question:

A student is studying the characteristics of waves. They measure the time it takes for a wave to travel a distance of 3 meters and find it to be 6 seconds. The student then measures the distance between two consecutive crests of the wave and finds it to be 2 meters. Determine the following wave characteristics:

a) What is the frequency of the wave? b) What is the period of the wave? c) What is the speed of the wave?

Answer:

a) To find the frequency of a wave, we can use the formula:

frequency (f) = 1 / period (T)

The period of a wave is the time it takes for one complete cycle or wave oscillation. In this case, the time taken for one complete cycle is the same as the time measured for the wave to travel 3 meters, which is 6 seconds.

frequency (f) = 1 / 6s

frequency (f) = 0.1667 Hz

Therefore, the frequency of the wave is 0.1667 Hz.

b) To find the period of a wave, we can use the formula:

period (T) = 1 / frequency (f)

Plugging in the frequency we just calculated:

period (T) = 1 / 0.1667 Hz

period (T) = 6s

Therefore, the period of the wave is 6 seconds.

c) The speed of a wave can be calculated using the formula:

speed (v) = wavelength (λ) × frequency (f)

The wavelength (λ) is the distance between two consecutive crests of the wave, which is measured to be 2 meters.

speed (v) = 2m × 0.1667 Hz

speed (v) = 0.3334 m/s

Therefore, the speed of the wave is 0.3334 m/s.

In summary:

a) The frequency of the wave is 0.1667 Hz. b) The period of the wave is 6 seconds. c) The speed of the wave is 0.3334 m/s.