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kchurchi
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Homework Statement
Sound Wavelength From String
During a concert a pianist hits a key that sets up a standing wave in a piano string that is vibrating in its fundamental mode. The string is 0.5 m long, has a mass density of 0.002 kg/m and is held under a tension of 120 N. What is the wavelength of the sound wave heard by the listener? The speed of sound in air is 343 m/s.
v (sound) = 343 m/s
L (length) = 0.5 m
d (mass density) = 0.002 kg/m
T (tension) = 120 N
λ (wavelength) = unknown
Homework Equations
v = f*λ = ω/k
f = frequency
k = spring constant
ω = angular frequency
v = √(T/(m/L))
T = force of tension
m = mass
L = length
The Attempt at a Solution
At first I attempted a solution using the second equation provided, however I am not quite sure what I would be solving for since the speed of sound in air is provided. Using the second equation I find the speed of the wave itself, but I am not sure how to apply the two speeds to finding the wavelength of the sound wave? Please help me with this problem!
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