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

Answer 1

Answer: (B)

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