Question

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

• A. $320m/s,80Hz$
  
• B. $320m/s,120Hz$
  
• C. $180m/s,120Hz$
  
• D. $180m/s,80Hz$
  

Answer 1

The correct option is A $320m/s,80Hz$


Given, length of the string, $L=2m$
Frequency of the vibrator, $f=240Hz$
Due to vibrator string vibrates in third harmonic mode,
$f_n=n\left(\frac{v}{2L}\right)$

$3\left(\frac{v}{2L}\right)=240$


$3\left(\frac{v}{2\times 2}\right)=240$

$v=320m/s$
Fundamental frequency of the wave, $f=\frac{v}{2L}$

$f=\frac{320}{2\times 2}=80Hz$

Final answer: (d)