A vibrator attached and resting on the surface of water generates plane water waves and its propagation is found to take 50 seconds to reach a floating cork 65 cm away. If the cork subsequently vibrates with SHM of a period 3.8 seconds, determine the wavelength of the water waves produced by the vibrator.
you know the velocity of propagation: .65m/50sec
frequency*lambda=velocity
To determine the wavelength of the water waves produced by the vibrator, we need to use the formula:
v = λ / T
where:
v is the speed of the wave,
λ is the wavelength, and
T is the period of the wave.
First, let's determine the speed of the wave. We know that the wave took 50 seconds to reach the cork, which is a distance of 65 cm. The speed of the wave can be calculated as:
v = d / t
v = 65 cm / 50 s
v = 1.3 cm/s
Now, we can substitute the values into the wavelength formula:
1.3 cm/s = λ / 3.8 s
Rearranging the equation to solve for the wavelength, we have:
λ = v * T
λ = 1.3 cm/s * 3.8 s
λ = 4.94 cm
Therefore, the wavelength of the water waves produced by the vibrator is approximately 4.94 cm.