A string fixed at both ends is 8.71 m long and has a mass of 0.119 kg. It is subjected to a tension of 92.0 N and set oscillating.
(a) What is the speed of the waves on the string?
(b) What is the longest possible wavelength for a standing wave?
(c) Give the frequency of that wave.
(a) V = sqrt (T/d)
T = 92 N
d = lineal density (mass divided by length)
(b) Twice the string length
(c) V/(wavelength)
Thanks I got it now.
To find the answers to these questions, we need to use the wave equation and some formulas related to waves on a string. Let's break down the questions and find the solutions step by step.
(a) What is the speed of the waves on the string?
The speed of waves on a string can be determined by the wave equation:
v = √(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.
To find the linear mass density, we divide the mass of the string (m) by its length (L):
μ = m/L
Substituting the given values, we have:
μ = 0.119 kg / 8.71 m
Now, we can calculate the speed of the wave:
v = √(T/μ) = √(92.0 N / (0.119 kg / 8.71 m)) = √(92.0 N * (8.71 m / 0.119 kg))
Calculate this expression to find the speed of the wave on the string.
(b) What is the longest possible wavelength for a standing wave?
The longest possible wavelength for a standing wave on a string is twice the length of the string:
λ_longest = 2L
Substitute the given length, L = 8.71 m, and calculate the longest possible wavelength.
(c) Give the frequency of that wave.
The frequency of a wave is related to its speed and wavelength by the equation:
f = v/λ
Substitute the calculated speed of the wave and the longest possible wavelength to find the frequency of the wave.
Remember to properly convert units, if necessary, to ensure consistency throughout the calculations.