In a standing wave, the distance between consecutive nodes corresponds to half a wavelength (λ/2). Thus, the distance between the first and fourth nodes is equal to 2.4 meters, which is equivalent to 1.5 times the wavelength (1.5 * λ).
We can set up the following equation:
2.4 meters = 1.5 * λ
To find the wavelength (λ), we can solve for it:
λ = 2.4 meters / 1.5 λ = 1.6 meters
Therefore, the wavelength of the wave is 1.6 meters.
To calculate the speed of the waves, we can use the wave equation:
v = λ * f
where: v = velocity of the waves λ = wavelength f = frequency
Given that the frequency is 60 Hz and the wavelength is 1.6 meters, we can substitute these values into the equation to find the velocity:
v = 1.6 meters * 60 Hz v = 96 meters/second
Hence, the speed of the waves is 96 meters per second.