Physics, asked by Rohithrocket1279, 1 month ago

The lower A on a piano has a frequency of 27.5 Hz. If the tension in the 2.0-m-long string is 304 N and one-half wavelength occupies the string, what is the mass of the string?

Answers

Answered by nitinchaudhari1254
1

Answer:

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Answered by tiwariakdi
1

The mass of the string is 0.05 kg.

A wave on a string moves at a specific pace because of:

v = \sqrt{T/\mu}

where

v is the speed of the wave,

T is the tension in the string,

μ is the string linear mass density.

The wave's frequency is determined by:

f = n ×  v/2L

where

n is the harmonic number,

L is the length of the string,

v is the speed of the wave.

The wavelength is twice as long as the string at the fundamental frequency (n=1), so:

λ = 2L/n = 2L

The wavelength of the harmonic with a half wavelength is four times the length of the string, so:

λ = 2L/n = 4L

The harmonic with a half-wavelength frequency is:

f = n ×  v/2L = v/λ = v/4L

The lower A on a piano has a frequency of 27.5 Hz, therefore

v/4L = 27.5 Hz

By solving for v:

v = 4L ×  27.5 Hz = 110 Hz

By substituting into the expression for the speed of the wave:

110 Hz = \sqrt{(T/\mu)}

By squaring both sides:

12100 Hz^2 = T/μ

By substituting T=304 N:

12100 Hz^2 = 304 N/μ

By solving for μ:

μ = 304 N / 12100 Hz^2 = 0.025 kg/m

The string has a linear mass density of 0.025 kg/m.

Given that the string is 2.0 m in length, the mass of the string is:

m = μ ×  L

m = 0.025 kg/m × 2.0 m

m = 0.05 kg

For similar question on mass of substance,

https://brainly.in/question/23620904

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