What is the wavelength of a standing wave in cm, if the separation between two adjacent nodes is 13.7cm?
To find the wavelength of a standing wave, we need to know the distance between two adjacent nodes. In this case, the separation between two adjacent nodes is given as 13.7 cm.
The distance between two adjacent nodes in a standing wave is equal to half a wavelength. Therefore, we can calculate the wavelength by multiplying the distance between two adjacent nodes by 2.
Wavelength = 2 * Distance between adjacent nodes
Wavelength = 2 * 13.7 cm
Wavelength = 27.4 cm
Therefore, the wavelength of the standing wave is 27.4 cm.
To find the wavelength of a standing wave, we can use the formula:
λ = 2L/n
Where:
- λ is the wavelength of the wave
- L is the separation between two adjacent nodes
- n is the number of nodes (including both the endpoints)
In this case, the separation between two adjacent nodes is given as 13.7 cm. Therefore, L = 13.7 cm.
Now, we need to find the value of n. The number of nodes in a standing wave is equal to the number of half-wavelengths that fit within the total length of the wave. Since a standing wave consists of a node at each end, the total number of nodes would be twice the number of half-wavelengths.
So, n = 2.
Now, we can substitute these values into the formula:
λ = 2L/n
= 2(13.7 cm)/(2)
= 13.7 cm
Therefore, the wavelength of the standing wave is 13.7 cm.