A standing is generated by two waves which have a velocity of 20 m/s, and go through 10 cycles in 2 seconds. How far is it from the 2nd node to the 7th node of standing wave?
The frequency of each of the two waves is f = 10/2 = 5 Hz and wavelength is V/f = 4 meters. The distance between nodes of a standing wave is half a wavelengh (2 meters). There are five half-waves between the second and seventh node.
Put it all tgether for the answer.
To determine the distance between the 2nd and 7th nodes of a standing wave, we need to find the wavelength of the wave.
The formula to calculate wavelength is:
wavelength (λ) = velocity (v) / frequency (f)
We know the velocity (v) is 20 m/s, but we need to find the frequency (f) to calculate the wavelength.
Frequency is defined as the number of cycles (or oscillations) per second. In this case, we are given that there are 10 cycles in 2 seconds. To find the frequency, we divide the number of cycles by the time:
frequency (f) = 10 cycles / 2 seconds = 5 Hz
Now that we have the frequency, we can calculate the wavelength:
wavelength (λ) = 20 m/s / 5 Hz = 4 meters
The wavelength of the wave is 4 meters.
In a standing wave, the distance between adjacent nodes (points where the wave undergoes constructive or destructive interference) is equal to half of the wavelength (λ/2).
Distance between the 2nd and 7th nodes = (7 - 2) * (λ/2)
= 5 * (4/2)
= 5 * 2
= 10 meters
Therefore, the distance between the 2nd and 7th nodes of the standing wave is 10 meters.