Question

A water wave is 3m tall. Taking a picture of the wave, you measure 7m between peaks. With your stopwatch, you measure .8 seconds between a peak and a trough. Write the wave function for this water wave. Ignore the initial phi.

Answer 1

The water wave function is given as
`y(x,t) = 3 sin((2\pi )/(7)(x +0.875t))`

Step-by-step explanation:

Water waves are surface waves, which is a mixture of longitudinal and transverse waves.

The general wave equation is given as;

`y(x,t) = A sin((2\pi )/(\lambda)(x +vt))`

where;

A is the amplitude = 3 m

λ is one wavelength = 7 m

t is period for one complete oscillation, T = 8 s

v is the velocity of the wave;

for each period, the wave travels one wavelength, v = λ/T = 7/8 = 0.875m/s

`y(x,t) = 3 sin((2\pi )/(7)(x +0.875t))`

Therefore, the water wave function is given as
`y(x,t) = 3 sin((2\pi )/(7)(x +0.875t))`