Question

A person lying on an air mattress in the ocean rises and falls through one complete cycle every five seconds. The crests of the wave causing the motion are 20.0 mapart. Determine (a) the frequency and (b) the speed of the wave. (Cutnell 16.6)

Answer 1

The frequency of the wave is 0.2 Hz, and the speed of the wave is 4.0 m/s, as determined by the given cycle time of 5 seconds and the crest distance of 20.0 meters.

Step-by-step explanation:

A person lying on an air mattress in the ocean rises and falls through one complete cycle every five seconds. To determine the frequency and the speed of the wave, we can apply the basic wave formulas.

Frequency of the Wave

The frequency of a wave (f) is defined as the number of cycles per second. Since one cycle takes 5 seconds, the frequency is :

f = 1/T = 1/5 s = 0.2 Hz

Speed of the Wave

The speed of a wave (v) can be determined by multiplying the frequency by the wavelength (λ). Given that the crests of the wave are 20.0 meters apart (which is the wavelength), the speed is:

v = f λ = 0.2 Hz × 20.0 m = 4.0 m/s

Answer 2

a) the frequency of the wave is 0.2 Hz

b) the speed of the wave 4 m/s

Step-by-step explanation:

Given that;

time period = to complete one cycle t = 5 sec

frequency f = 1/t

frequency f = 1 / 5sec

f = 0.2 Hz

Therefore the frequency of the wave is 0.2 Hz

b)

speed of wave V = λf

given that our wavelength is 20.0 m

we substitute

speed of wave V = 20.0 × 0.2

speed of wave V = 4 m/s

Therefore, the speed of the wave 4 m/s