three antinodes witha peak to peak displacement of 3 cm are observed on a vibrating string of length l and linear density the hanging mass is m what is the velocity of the propagation of transverse waves of the string
To find the velocity of the propagation of transverse waves on a vibrating string, we can use the formula:
v = √(T/μ)
where:
v is the velocity of the wave,
T is the tension in the string, and
μ is the linear mass density (mass per unit length) of the string.
In this case, we are given the displacement of the antinodes (peak to peak displacement), but we need the tension in the string and the linear mass density.
Let's start by finding the tension in the string.
The tension in the string can be calculated using the formula:
T = m × g
where:
T is the tension in the string,
m is the mass hanging from the string,
and g is the acceleration due to gravity.
In this case, the hanging mass is given as "m". We assume that it is directly hanging from the string, causing its tension. So, we can use the given "m" as the mass in the formula.
Now, let's find the linear mass density of the string.
The linear mass density of the string is given by the formula:
μ = m/L
where:
μ is the linear mass density,
m is the mass hanging from the string, and
L is the length of the string.
We are given the length of the string as "l". However, it's important to note that we need the total length of the string, including any additional length beyond the vibrating region. So, we'll use "l" directly as the length.
Now that we have the tension (T) and the linear mass density (μ), we can calculate the velocity of the wave using the formula:
v = √(T/μ)
Plug in the values and solve for v.