Question 292: Waves

Question

A string is under tension of 180 N and mass per unit length $2 	imes 10^{-3} \mathrm{Kg} / \mathrm{m}$. It produces two consecutive resonant frequencies with a tuning fork, which are 375 Hz and 450 Hz . The mass of the string is

Accepted Answer

To determine the mass of the string, we can follow these steps:
Calculate the Fundamental Frequency:
The fundamental frequency is the difference between the two consecutive resonant frequencies:
$    	ext{Fundamental frequency} = f_2 - f_1 = 450 \, 	ext{Hz} - 375 \, 	ext{Hz} = 75 \, 	ext{Hz}    $
Use the Formula for Frequency:
The frequency $ f $ of a vibrating string is given by:
$    f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}    $
where $ T $ is the tension in the string, $\mu$ is the mass per unit length, and $ L $ is the length of the string.
Rewrite the Equation and Solve for $ L $:
Plug in the known values:
$    75 = \frac{1}{2L} \sqrt{\frac{180}{2 	imes 10^{-3}}}    $
Solving for $ L $:
$    L = 2 \, 	ext{m}    $
Find the Mass ($ m $) of the String:
Using the relationship for mass per unit length:
$    \mu = \frac{m}{L}    $
Rearrange to find $ m $:
$    m = \mu 	imes L = (2 	imes 10^{-3} \, 	ext{Kg/m}) 	imes 2 \, 	ext{m} = 4 	imes 10^{-3} \, 	ext{Kg} = 4 \, 	ext{grams}    $
Therefore, the mass of the string is 4 grams.

Answer

1 gram

Answer

2 gram

Answer

3 gram

Answer

4 gram

Waves

A string is under tension of 180 N and mass per unit length 2 \times 10^{-3} \mathrm{Kg} / \mathrm{m}. It produces two consecutive resonant frequencies with a tuning fork, which are 375 Hz and 450 Hz . The mass of the string is

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