College

(a) Find the speed of waves on a violin string with a mass of 717 mg and a length of 24.3 cm if the fundamental frequency is 980 Hz.

(b) What is the tension in the string?

For the fundamental, what is the wavelength of:

(c) the waves on the string?

(d) the sound waves emitted by the string? (Take the speed of sound in air to be 343 m/s.)

Answer :

Answer:

a)v = 476.28 m / s
, b) T = 6.69 10⁵ N
, c) λ = 0.486 m
, d) λ = 0.35 m

Explanation:


a) The speed of a wave on a string is

v = √T /μ

also all the waves fulfill the relationship

v = λ f


they indicate that the fundamental frequency is f = 980 Hz.


The wavelength that is fixed at its ends and has a maximum in the center

L = λ / 2

λ = 2L


we substitute

v = 2 L f

let's calculate

v = 2 0.243 980

v = 476.28 m / s

b) The tension of the rope

T = v² μ


the density of the string is

μ = m / L

T = v² m / L

T = 476.28² 0.717 / 0.243

T = 6.69 10⁵ N



c) λ = 2L

λ = 2 0.243

λ = 0.486 m

d) The violin has a resonance process with the air therefore the frequency of the wave in the air is the same as the wave in the string. Let's find the wavelength in the air

v = λ f

λ= v / f

λ = 343/980

λ = 0.35 m

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