A string fixed at both the ends is oscillating in its 3rd overtone. If the tension in the string is 10N, its mass is 1gm and length is 4m. Find the frequency (in Hz )?

Question

A string fixed at both the ends is oscillating in its 3rd overtone. If the tension in the string is 10N, its mass is 1gm and length is 4m. Find the frequency (in Hz )? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-q4buttdmm6sbzycd.jpg" /> 3rd overtone, 4th harmonic T=10N m=1gmL=4m v=√(T/μ )=200ms- 1 4× (λ /2)=4 λ =2m n=(200/2)=100Hz

Q. A string fixed at both the ends is oscillating in its $3^{r d}$ overtone. If the tension in the string is $10 N,$ its mass is $1 g m$ and length is $4 m .$ Find the frequency (in $Hz$ )?

$3^{r d}$ overtone, $4^{t h}$ harmonic
$T = 10 N$
$m = 1 g m L = 4 m$
$v = \frac{T}{μ} = 200 m s^{- 1}$
$4 \times \frac{λ}{2} = 4$
$λ = 2 m$
$n = \frac{200}{2} = 100 Hz$

Q. A string fixed at both the ends is oscillating in its 3rd overtone. If the tension in the string is 10N, its mass is 1gm and length is 4m. Find the frequency (in Hz )?

3rd overtone, 4th harmonic T=10N m=1gmL=4m v=μT​​=200ms−1 4×2λ​=4 λ=2m n=2200​=100Hz

Q. A string fixed at both the ends is oscillating in its $3^{r d}$ overtone. If the tension in the string is $10 N,$ its mass is $1 g m$ and length is $4 m .$ Find the frequency (in $Hz$ )?

$3^{r d}$ overtone, $4^{t h}$ harmonic
$T = 10 N$
$m = 1 g m L = 4 m$
$v = \frac{T}{μ} = 200 m s^{- 1}$
$4 \times \frac{λ}{2} = 4$
$λ = 2 m$
$n = \frac{200}{2} = 100 Hz$