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EleoNora [17]
3 years ago
6

Two cello strings, with the same tension and length, are played simultaneously. Their fundamental frequencies produce audible be

ats with a frequency of 8 Hz. The string with the lower pitch (frequency) is tuned to an “A” (a frequency of 220 Hz). What is the approximate ratio of the linear mass density μ of the string with the higher pitch to that of the string with the lower pitch?
Physics
1 answer:
qwelly [4]3 years ago
3 0

Explanation:

Let f₁ is the fundamental frequency, f_1=8\ Hz

Lower pitch frequency, f_2=220\ Hz

Fundamental frequency is, f_1=\dfrac{1}{2L}\sqrt{\dfrac{T}{\mu_1}}.....(1)

Lower frequency is, f_2=\dfrac{1}{2L}\sqrt{\dfrac{T}{\mu_2}}..............(2)

Dividing equation (1) and (2) as :

\dfrac{f_1}{f_2}=\sqrt{\dfrac{\mu_2}{\mu_1}}

\dfrac{\mu_2}{\mu_1}=(\dfrac{f_1}{f_2})^2

\dfrac{\mu_2}{\mu_1}=(\dfrac{8}{220})^2

\dfrac{\mu_2}{\mu_1}=0.00132

So, the ratio of  linear mass density μ of the string with the higher pitch to that of the string with the lower pitch is 0.00132. Hence, this is the required solution.

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