A string is stretched between two supports that are L = 0.9 m apart. It resonates at a frequency of f = 410 Hz with a standing wave pattern that has two nodes between the two supports.
(a) Find the wavelength λ in meters.
(b) Suppose that the tension, T, in the string is increased by a factor of 4. What is the new frequency f' in Hz if the string vibrates with the same standing wave pattern as in the drawing above?
The wire length is one half wavelength
wave speed is proportional to the square root of tension, so wave speed is doubled here.
f*lambda=speed, so if lambda is constant, speed doubled, f must...
I got the wavelength to be (2/3)L which gives you .6 and that's correct, but I can't get the second part right
To find the wavelength λ, we can use the formula:
λ = 2L/n
where L is the distance between the supports and n is the number of nodes (in this case, two nodes).
(a) Plugging in the values, we have:
λ = 2(0.9m)/(2)
λ = 0.9m
So, the wavelength of the string is 0.9 meters.
(b) To find the new frequency f', we can use the formula:
f' = f√(T'/T)
where T' is the new tension and T is the initial tension.
In this case, the initial tension T is not given. However, since the standing wave pattern remains the same, we can assume that the tension in the string before the increase is the same as the tension after the increase.
Therefore, we can write:
f' = f√(T'/T) = f√(4/1) = 2f
Substituting the given frequency f = 410 Hz, we can calculate the new frequency f':
f' = 2(410 Hz) = 820 Hz
So, the new frequency f' is 820 Hz.