A string on a violin is stretched between two points 20.00 cm apart with a tension of 120.0 N. The mass/length of the string is 0.002000 kg/m. The frequency of the mode next higher than the fundamental mode is
Question
A string on a violin is stretched between two points 20.00 cm apart with a tension of 120.0 N. The mass/length of the string is 0.002000 kg/m. The frequency of the mode next higher than the fundamental mode is
Solution
The problem is asking for the frequency of the mode next higher than the fundamental mode, which is the second harmonic or the first overtone.
The fundamental frequency (f1) of a vibrating string is given by the formula:
f1 = (1/2L) * sqrt(T/μ)
where: L = length of the string = 20.00 cm = 0.2 m T = tension in the string = 120.0 N μ = mass per unit length = 0.002000 kg/m
Substituting these values into the formula gives:
f1 = (1/(2*0.2)) * sqrt(120/0.002) = 122.47 Hz
The frequency of the mode next higher than the fundamental mode (f2) is twice the fundamental frequency. Therefore:
f2 = 2 * f1 = 2 * 122.47 Hz = 244.94 Hz
So, the frequency of the mode next higher than the fundamental mode is approximately 244.94 Hz.
Similar Questions
Two strings on a violin are stretched between two points 20.0 cm apart. The mass per length of the strings are the same. If the ratio of the frequencies of the fundamental modes is 1.5 to 1.0, then what is the ratio of the tensions in the strings?
A string on a guitar is stretched between two points 30.0 cm apart with a tension of 100 N. The mass/length of the string is 0.003 kg/m. The wavelength of the mode of vibration with the lowest frequency is
A string with a mass/length of 0.00200 kg/m is stretched between two points with a tension of 120 N. If the fundamental frequency is 440 Hz, then what is the distance between the two points?
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 string with a mass per length of 2.00 g/m is stretched with a force of 120 N between two points that are 0.400 m apart. The fundamental frequency of the stretched string is in tune with the frequency of the second mode of an organ pipe filled with air and open at both ends. The speed of sound in air at 0°C is 331 m/s. What is the length of the organ pipe?
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.