A distance of 5.00 cm is measured between two adjacent nodes of a standing wave on a 20.0 cm long string.
A) In which harmonic number is the string vibrating?
4
20/5=4
To determine the harmonic number in which the string is vibrating, we can use the formula:
λ = (2L) / n
where:
λ = wavelength
L = length of the string
n = harmonic number
In this case, the measured distance between two adjacent nodes represents one-half of the wavelength, so the wavelength can be calculated by multiplying 5.00 cm by 2. Thus:
λ = 5.00 cm × 2 = 10.00 cm
Now, we can plug the known values into the formula and solve for the harmonic number (n):
10.00 cm = (2 × 20.0 cm) / n
Multiplying both sides of the equation by n:
10.00 cm × n = 2 × 20.0 cm
Dividing both sides of the equation by 10.00 cm:
n = (2 × 20.0 cm) / 10.00 cm
Simplifying:
n = 40.0 cm / 10.00 cm
n = 4
Therefore, the string is vibrating in the 4th harmonic.
To determine the harmonic number in which the string is vibrating, we need to understand the concept of harmonics in standing waves.
In a standing wave, nodes are points of no displacement, whereas antinodes are points of maximum displacement. The distance between consecutive nodes (or antinodes) is one wavelength.
We are given that the distance between two adjacent nodes is 5.00 cm, which means that the length of one complete wavelength is 5.00 cm.
We can use the formula to find the wavelength of a standing wave:
Wavelength (λ) = 2 * Length of string (L) / Harmonic number (n)
Given that the length of the string (L) is 20.0 cm and the wavelength (λ) is 5.00 cm, we can rearrange the formula to solve for the harmonic number (n):
n = 2 * L / λ
Substituting the values into the equation:
n = 2 * 20.0 cm / 5.00 cm
n = 40.0 cm / 5.00 cm
n = 8
Therefore, the string is vibrating in the 8th harmonic.