The displacement from the equilibrium caused by a wave on a string is given by: y(x,t) = (-0.00200 m)sin[(40m^-1)x-(800s^-1)t]. What is the number of waves in 1 m?
when is 40 x = 2 pi (full wavelength) ??
when x = pi/20 meters
that is the wave length
How many wave lengths in 1 meter ?
20/pi
To find the number of waves in 1 meter, we need to determine the wavelength (λ) of the wave. The wavelength represents the distance between two consecutive points in a wave that are in phase, meaning they have the same displacement.
In the given expression, y(x, t) = (-0.00200 m)sin[(40m^-1)x-(800s^-1)t], we have the term (40m^-1)x, which represents the spatial component of the wave. The inverse of this value (1/(40m^-1)) will give us the wavelength.
To find the inverse, we use the formula:
Inverse = 1 / Value
Therefore, the inverse of (40m^-1) is:
Inverse = 1 / (40m^-1) = (1m^-1) / 40
Now, if we have the wavelength (λ), the number of waves in 1 meter can be determined by dividing 1 meter by the wavelength.
Number of waves = 1 meter / wavelength
Plugging in the value of the inverse wavelength:
Number of waves = 1 meter / (1m^-1) / 40
Simplifying the expression:
Number of waves = 1 meter × 40m / 1
Finally, we find that the number of waves in 1 meter is 40 waves.