The wave function for a certain standing wave on a string is given by y(x,t) = A0 sin(k0x)sin(ù0t) where k0 = 3ð rad/m and ù0 = 6ð rad/s . What is the wavelength of the standing wave?
To find the wavelength of the standing wave, we need to identify the relationship between the wave function and the wavelength. In this case, the standing wave is represented by the equation:
y(x,t) = A0 sin(k0x) sin(ù0t)
where y(x,t) represents the displacement of the string at position x and time t, A0 is the amplitude of the wave, k0 is the wave number, and ù0 is the angular frequency.
The wave number (k0) is related to the wavelength (λ) through the equation:
k0 = 2π / λ
where λ represents the wavelength.
From the given information, we have the wave number (k0 = 3π rad/m).
To find the wavelength, rearrange the equation as follows:
k0 = 2π / λ
Multiply both sides by λ:
λ * k0 = 2π
Divide both sides by k0:
λ = 2π / k0
Substitute the value of k0:
λ = 2π / (3π rad/m)
Simplify:
λ = 2 / 3 m
Therefore, the wavelength of the standing wave is 2/3 meters.