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.
I will be happy to critique your thinking. on part b, use the wave equation.
To answer these questions, we need to use the formulas and concepts related to waves on a string.
(a) The speed of waves on a string can be calculated using the formula:
v = √(T / μ)
where:
v is the speed of the waves,
T is the tension in the string, and
μ is the linear density of the string.
In this case, the tension (T) is 92.0 N and the linear density (μ) can be calculated by dividing the mass (m) by the length (L) of the string:
μ = m / L = 0.119 kg / 8.71 m
Substituting the values into the formula:
v = √(92.0 N / (0.119 kg / 8.71 m))
By evaluating the expression, you can find the speed of the waves on the string.
(b) The longest possible wavelength for a standing wave on the string is equal to twice the length of the string:
λ_max = 2L
Again, substituting the value of L into the formula will give you the longest possible wavelength.
(c) The frequency (f) of the wave can be calculated using the formula:
f = v / λ
where:
f is the frequency,
v is the speed of the wave, and
λ is the wavelength.
From part (b), you have the value of the longest possible wavelength. You can plug these values into the formula to find the frequency of the wave.
Remember to use the appropriate units throughout the calculations.