Respuesta :
Answer:
velocity of standing wave = 0.34 * frequency
Velocity of transverse wave = 40.724 m/sec
Explanation:
Given data
The linear mass density = 1.3 * 10^-3 kg/m
number of antinodes = 10
Total string length = 1.7 meters
first we have to calculate the tension in the string
= Mg = 0.22 * 9.81 = 2.156 N
next we will determine the velocity of the wave
= [tex]\sqrt{\frac{T}{linear mass density} }[/tex] = [tex]\sqrt{} \frac{2.156}{1.3*10^{-3} }[/tex] = 40.724 m/sec
The distance between two antinodes = 1.7 / 10 = 0.17 m
next we calculate the wavelength = distance between antinodes * 2 = 0.34m
There is no difference between the transverse wave velocity calculated from the string material properties and the one following from the standing wave configuration and this is because the Frequency of vibration of the standing wave is not given
Difference between the transverse wave velocity is 0.34f m/sec.
Wave velocity based problem:
What information do we have:
Number of antinodes = 10
Length of string = 1.7 m
Mass = 0.22 kg
String linear density = 1.3 gram/meter
Using equation v = √( T / μ )
v = √(mg / μ)
v = √(0.22 × 9.8) / (1.3 × 10⁻³ )1/2
v = 40.7 m/sec
Wavelength of the wave in string λ = 2L / n
Wavelength of the wave in string λ = (2 × 1.7) / 10
Wavelength of the wave in string λ = 0.34 m
Wave velocity v = fλ
Wave velocity v = 0.34f m/sec
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