A string of length 8 m fixed at both the ends has a tension of 49 N and a mass 0.04 kg.
Find the speed of transverse waves on this string.
You should have been taught about this formula for the wave speed, V.
V = sqrt (T/d)
T = tension = 49 N
d = density per length = 0.04/8 = 0.005 kg/m
V = sqrt(49/.005) = 99 m/s
To find the speed of transverse waves on the string, we need to use the wave equation:
v = √(T/μ)
Where:
v = speed of transverse waves
T = tension in the string
μ = linear mass density of the string
The tension in the string is given as 49 N and the mass of the string is given as 0.04 kg.
The linear mass density (μ) is calculated by dividing the mass of the string by its length (L):
μ = m/L
Since the length of the string is not given, we cannot calculate the linear mass density and therefore cannot find the speed of transverse waves.
To find the speed of transverse waves on this string, we can use the equation:
v = √(T / μ)
where:
v = speed of transverse waves
T = tension in the string
μ = mass per unit length of the string
First, we need to calculate the mass per unit length of the string. Since the string has a mass of 0.04 kg and a length of 8 m, we can find μ using the formula:
μ = m / L
where:
m = mass of the string
L = length of the string
μ = 0.04 kg / 8 m = 0.005 kg/m
Now we can substitute the values of T and μ into the equation to find the speed:
v = √(49 N / 0.005 kg/m)
v = √(9800 m²/s² / 0.005 kg/m)
v = √(1960000 m²/s² / kg/m)
v ≈ 140 m/s
Therefore, the speed of transverse waves on this string is approximately 140 m/s.