A particular guitar wire is 30.0 cm long and vibrates at a frequency of 196 Hz when no finger is placed on it. The next higher notes on the scale are 220 Hz, 247 Hz, 262 Hz and 294 Hz. How far from the end of the string must the finger be placed to play these notes ?

Open in App

Solution

$l_{1} = 30 c m = 0.3 m$
$f_{1} = 196 H z, f_{2} = 220 H z$

we know $f α (1 / l)$ (as V is constant for a medium)
$\Rightarrow \frac{f_{1}}{f_{2}} = \frac{l_{2}}{l_{1}} \Rightarrow l_{2} = 26.7 c m$

Again $f_{3} = 247 H z$
$\Rightarrow \frac{f_{3}}{f_{1}} = \frac{l_{1}}{l_{3}} \Rightarrow \frac{0.3}{l_{3}}$
$\Rightarrow l_{3} = 0.224 m = 22.4 c m$ and $l_{3} = 20 c m$

Suggest Corrections

Similar questions

A particular guitar wire is 30.0 cm long and vibrates at a frequency of 196 Hz when no finger is placed on it. The next higher notes on the scale are 220 Hz, 247 Hz, 262 Hz and 294 Hz. How far from the end of the string must the finger be placed to play these notes?

Q. A certain string (fixed at one end and free at the other end) can vibrate at several frequencies, the lowest of which is

200 Hz

. What are next two higher frequencies to which it vibrates?

The frequencies of notes given by flute, guitar and trumpet are respectively 400 Hz, 200 Hz and 500 Hz. Which one of these has the highest pitch ?

Join BYJU'S Learning Program

A particular guitar wire is 30.0 cm long and vibrates at a frequency of 196 Hz when no finger is placed on it. The next higher notes on the scale are 220 Hz, 247 Hz, 262 Hz and 294 Hz. How far from the end of the string must the finger be placed to play these notes ?

l1=30cm=0.3mf1=196Hz,f2=220Hzwe know fα(1/l) (as V is constant for a medium)⇒f1f2=l2l1⇒l2=26.7cmAgain f3=247Hz⇒f3f1=l1l3⇒0.3l3⇒l3=0.224m=22.4cm and l3=20cm