The speed (v) of an ocean wave depends on its wavelength ë (measured in meters) and the gravitational field strength g (measured in m/s62) according to the formula v = Këˣgʸ where K is a dimensionless constant. Find the value of the exponent x and y.
To find the value of the exponents x and y in the formula v = Këˣgʸ, we need to use the given information. In this case, we know that the speed of an ocean wave depends on its wavelength (ë) and the gravitational field strength (g).
To determine the value of the exponent x, we can look at the units involved. The wavelength is measured in meters (m), and the speed of the wave is also measured in meters per second (m/s). Since the units of wavelength and speed are the same, we can conclude that the exponent x must be 1. This means the equation becomes v = Këgʸ.
To determine the value of the exponent y, we need to consider the units involved. The gravitational field strength (g) is measured in m/s², and the speed of the wave is measured in m/s. To cancel out the units of m/s² from the equation, the exponent y must be -1. This means the final equation becomes v = Këg⁻¹.
To summarize, the values of the exponents are x = 1 and y = -1. Therefore, the formula for the speed of an ocean wave in terms of its wavelength and gravitational field strength is v = Këg⁻¹.