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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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