The wave crests generated in a ripple tank are 15mm apart and the frequency of the vibrator is 20Hz.
If the frequency of the vibrator is trebled what is the spacing between the crest
divide 15mm by 3
Yes
lambda = v/T = f v
If velocity is constant that works. However watch out. In water gravity waves that only works when the depth is shallow compared to the wavelength in which case velocity is proportional to square root of depth.
When the water depth becomes greater than half a wavelength, the velocity becomes proportional to the square root of the wavelength
To find the spacing between the crests when the frequency of the vibrator is trebled, we need to determine the new wavelength.
We can use the formula for the relationship between frequency, velocity, and wavelength:
velocity = frequency * wavelength
The velocity of the waves in the ripple tank is constant, so we can set up the following equation:
velocity * original wavelength = (3 * original frequency) * new wavelength
Given that the original frequency is 20Hz and the original wavelength is 15mm, we can substitute these values and solve for the new wavelength.
velocity * 15mm = 3 * 20Hz * new wavelength
Since we don't have the value for the velocity, we can ignore it for the sake of this problem, as it cancels out on both sides of the equation.
15mm = 60Hz * new wavelength
Now, we can solve for the new wavelength:
new wavelength = 15mm / 60Hz
= 0.25mm
Therefore, when the frequency of the vibrator is trebled, the spacing between the crests will be 0.25mm.