Guitar Strings

Q.

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?

1. 30 cm, 20 cm, 10 cm, 5 cm

2. 26.7 cm, 23.8 cm, 22.4 cm, 20.0 cm

3. 23.8 cm, 22.4 cm, 20 cm, 10 cm

4. none of these

Q. Four wires of identical length, diameters and of the same material are stretched on a sonometer wire. If the ratio of their tension is $1:4:9:16$, then the ratio of their fundamental frequencies is

1. $16:9:4:1$
2. $4:3:2:1$
3. $1:4:2:16$
4. $1:2:3:4$

Q. The length of a sonometer wire AB is $110\text{cm}$. Where should the two bridges be placed (from A) to divide the wire into $3$ segments, whose fundamental frequencies are in the ratio of $1:2:3$ ?

1. $60\text{cm}$ and $90\text{cm}$
2. $30\text{cm}$ and $60\text{cm}$
3. $40\text{cm}$ and $80\text{cm}$
4. $30\text{cm}$ and $90\text{cm}$

Q. A V shaped-tube having unequal arm-lengths has water in it. A turning fork of frequency $550\text{Hz}$ can set up the air in the shorter arm into its fundamental mode of vibration and the same turning fork can set up the air in the longer arm into its first overtone of vibration. Find the lengths of the air column in both the arms.

[Neglect any end effect and assume that the speed of sound in air is $330{\text{ms}}^{-1}$. Take $L_1$ to be the length of shorter column and $L_2$ to be the length of longer column.]

1. $L_1=20\text{cm}$, $L_2=40\text{cm}$
2. $L_1=15\text{cm}$, $L_2=45\text{cm}$
3. $L_1=20\text{cm}$, $L_2=45\text{cm}$
4. $L_1=10\text{cm}$, $L_2=30\text{cm}$

Q. The length of a sonometer wire $\text{AB}$ is $110\text{cm}$. Where should the two bridges be placed (from $\text{A}$) to divide the wire into $3$ segments, whose fundamental frequencies are in the ratio of $1:2:3$ ?

1. $30\text{cm}$ and $90\text{cm}$
2. $40\text{cm}$ and $80\text{cm}$
3. $60\text{cm}$ and $90\text{cm}$
4. $30\text{cm}$ and $60\text{cm}$

Q.

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?

1. 26.7 cm, 23.8 cm, 22.4 cm, 20.0 cm

2. 30 cm, 20 cm, 10 cm, 5 cm

3. 23.8 cm, 22.4 cm, 20 cm, 10 cm

4. none of these

Q. Four wires of identical length, diameters and of the same material are stretched on a sonometer wire. If the ratio of their tension is $1:4:9:16$, then the ratio of their fundamental frequencies is

1. $16:9:4:1$
2. $4:3:2:1$
3. $1:4:2:16$
4. $1:2:3:4$

Q.

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?

1. 26.7 cm, 23.8 cm, 22.4 cm, 20.0 cm

2. 30 cm, 20 cm, 10 cm, 5 cm

3. 23.8 cm, 22.4 cm, 20 cm, 10 cm

4. none of these

Q. Four wires of identical length, diameters and of the same material are stretched on a sonometer wire. If the ratio of their tension is $1:4:9:16$, then the ratio of their fundamental frequencies is

1. $16:9:4:1$
2. $4:3:2:1$
3. $1:4:2:16$
4. $1:2:3:4$

Q. The length of a sonometer wire $\text{AB}$ is $110\text{cm}$. Where should the two bridges be placed (from $\text{A}$) to divide the wire into $3$ segments, whose fundamental frequencies are in the ratio of $1:2:3$ ?

1. $30\text{cm}$ and $90\text{cm}$
2. $40\text{cm}$ and $80\text{cm}$
3. $60\text{cm}$ and $90\text{cm}$
4. $30\text{cm}$ and $60\text{cm}$