A 0.220 kg string is attached to opposite sides of aroom that is 4.30 m across. If the string is pluckedand the resultant wave speed on the string is 18.0 m/s,what is the tension in the string?
Question
A 0.220 kg string is attached to opposite sides of aroom that is 4.30 m across. If the string is pluckedand the resultant wave speed on the string is 18.0 m/s,what is the tension in the string?
Solution
The speed of a wave on a string is given by the formula:
v = sqrt(T/μ)
where: v is the speed of the wave, T is the tension in the string, and μ is the linear mass density of the string.
We can rearrange this formula to solve for T:
T = μv²
The linear mass density μ of the string is its mass m divided by its length L:
μ = m/L
Substituting the given values:
μ = 0.220 kg / 4.30 m = 0.05116 kg/m
Now we can substitute μ and v into the formula for T:
T = 0.05116 kg/m * (18.0 m/s)² = 16.6 N
So the tension in the string is 16.6 Newtons.
Similar Questions
Transverse waves with a speed of 46.5 m/s are to be produced on a stretched string. A 4.30-m length of string with a total mass of 0.0600 kg is used.(a) What is the required tension in the string? N(b) Calculate the wave speed in the string if the tension is 8.00 N. m/s
The speed of a transverse wave on a string is 110 m s−1. The tension in the string is340 N. Calculate the mass per unit length of the string
A violin string has a wave speed of 62 m/s when it isplayed. If the string is 0.60 m long and has a tensionof 200.0 N, what is the mass of the string?
A rope with length 2.50 m and mass 0.10 kg is stretched and pulled to create transverse waves of frequency 40.0 Hz and wavelength of 0.750 m. How much tension is exerted on the rope?
The speed of a wave on a string is 150m/s when the tension is 120N. The percentage increase in the tension in order to raise the wave speed by 20% is?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.