A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is

Question

A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is (A) 320 m s- 1, 120 Hz (B) 320 text m s- 1, 80 Hz (C) 180 m s- 1, 80 Hz (D) 180 m s- 1, 120 Hz

Tardigrade Admin · Accepted Answer

For a string fixed at both the ends, f=(n/2 L)v For third harmonic, 240=(3/2 (. 2 .))v ⇒ v=(240 × 4/3) =320 ms- 1 Fundamental frequency f0=(1/2 L)v =(1/4)× 320 = 80 Hz

Q. A string $2.0 m$ long and fixed at its ends is driven by a $240 Hz$ vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is

$320 m s^{- 1}, 120 Hz$

$320 m s^{- 1}, 80 Hz$

$180 m s^{- 1}, 80 Hz$

$180 m s^{- 1}, 120 Hz$

For a string fixed at both the ends,
$f = \frac{n}{2 L} v$
For third harmonic, $240 = \frac{3}{2 ( 2 )} v$
$\Rightarrow v = \frac{240 \times 4}{3}$
$= 320 m s^{- 1}$
Fundamental frequency $f_{0} = \frac{1}{2 L} v$
$= \frac{1}{4} \times 320 = 80 Hz$

Q. A string 2.0m long and fixed at its ends is driven by a 240Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is

320ms−1,120Hz

320ms−1,80Hz

180ms−1,80Hz

180ms−1,120Hz