Guitar Strings

Q. The length of the wire between two ends of a sonometer is $100\text{cm}$. What should be the positions of two bridges (from left end of sonometer) below the wire so that the three segments of the wire have their fundamental frequencies in the ratio $1:3:5$

1. $\frac{1500}{23}\text{cm},\frac{500}{23}\text{cm}$
2. $\frac{1500}{23}\text{cm},\frac{300}{23}\text{cm}$
3. $\frac{300}{23}\text{cm},\frac{800}{23}\text{cm}$
4. $\frac{1500}{23}\text{cm},\frac{2000}{23}\text{cm}$

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 sonometer wire has a total length of $2\text{m}$ between the fixed ends. Where should the two bridges be placed, so that the three segments of the wire have fundamental frequencies in the ratio $1:3:5$ ?

1. $\frac{30}{23}\text{m}$ and $\frac{40}{23}\text{m}$ from one end.
2. $\frac{6}{23}\text{m}$ and $\frac{16}{23}\text{m}$ from other end.
3. $\frac{30}{23}\text{m}$ from one end and $\frac{6}{23}\text{m}$ from the other end.
4. $\frac{30}{23}\text{m}$ from one end and $\frac{10}{23}\text{m}$ from the other end.

Q. The fundamental frequency of a sonometer wire increases by 5 Hz if its tension is increased by 21%. Instead if the length of wire is decreased by 10%, then the fundamental frequency becomes

1. 45.45 Hz
2. 50 Hz
3. 55.55 Hz
4. None of the above

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 fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is $20$cm, the length of the open organ pipe is

1. $12.5$cm
2. $13.2$cm
3. $16$cm
4. $8$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 wire of length $L$ and mass per unit length $6.0\times {10}^{-3}{\text{kgm}}^{-1}$ is put under tension of $540\text{N}$. Two consecutive frequencies that resonates with it are : $420\text{Hz}$ and $490\text{Hz}$. Then the value of $L$ (in meters) is:

1. $\text{2.1 m}$
2. $\text{1.1 m}$
3. $\text{8.1 m}$
4. $\text{5.1 m}$

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. A sonometer wire has a length of $114$ cms between two fixed ends; Where should two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio $1:3:4$?

Q. A sonometer wire of length $1.5m$ is made of steel. The tension in it produces an elastic strain of $1\%$. What is the fundamental frequency of steel if density and elasticity of steel are $7.7\times {10}^{3}kg/m^3$ and $2.2\times {10}^{11}N/m^2$ respectively?

1. $178.2Hz$
2. $200.5Hz$
3. $770Hz$
4. $188.5Hz$

Q. The graph between object distance u and image distance v for a lens is given. The focal length of the lens is

1. 0.5 $\pm$0.05 cm
2. 5$\pm$ 0.1 cm
3. 0.5$\pm$ 0.1 cm
4. 5$\pm$ 0.05 cm

Q. A guitar string is $90cm$ long and has a fundamental frequency of $124Hz$. To produce a fundamental frequency of $186Hz$, the guitar should be pressed at ?

1. $30cm$
2. $20cm$
3. $10cm$
4. $60cm$

Q. A metre bridge is balanced with known resistance in the right gap and a metal wire in the left gap. If the metal wire is heated the balance point

1. shifts towards left
2. does not change
3. shifts towards right
4. may shift towards left or right depending on the nature of the metal

Q. If the tension and diameter of a sonometer wire of fundamental frequency n is doubled and density is halved then its fundamental frequency will become

1. n
2. $\frac{n}{\sqrt{2}}$
3. $\frac{n}{4}$
4. $\sqrt{2n}$

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. Two vibrating strings of the same material but lengths L and $2$L have radii $2$r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency $n_1$ and the other with frequency $n_2$. The ratio $n_1/n_2$ is given by.

1. $2$
2. $4$
3. $8$
4. $1$

Q.

A tuning fork vibrating with sonometre wire of length 20cm produces 5 beats per second . The beat frequency doesn't change if length of wire is changed to 21cm , the frequency of tuning fork is

1. 280
2. 190
3. 205
4. 210

Q. When the rms voltages $V_L,V_C$ and $V_R$ are measured respectively across the inductor L, the capacitor C and the resistor R in a series LCR circuit connected to an AC source, it is found that the ratio $V_L:V_C:V_R=1:2:3$. If the rms voltage of the AC source is 100 V, then $V_R$ is close to :

1. 50 V
2. 70 V
3. 90 V
4. 100 V

Q. A wire produces a fundamental frequency $n$ under a tension $T$. The wire is stretched to twice its length and kept under the same tension. The fundamental frequency of the wire is

1. $2n$
2. $n$
3. $n\sqrt{2}$
4. $\frac{n}{\sqrt{2}}$

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 ?

Q. A string on musical instrument is $50cm$ long and its fundamental frequency is $270Hz$. If the desired frequency of $1000Hz$ is to be produced, the required string length in $cm$ is

1. $13.5$
2. $5.4$
3. $10.8$
4. $2.7$

Q. When a stretched wire and a tuning fork are sounded together, $5$ beats per second are produced, when length of wire is $95cm$ or $100cm$, frequency of the fork is

1. $195Hz$
2. $100Hz$
3. $105Hz$
4. $90Hz$

Q. The bridge of a sonometer is slightly displaced so that the length of the wire is decreased by $0.5\%$ and the tension in the wire is increased by $1\%$. The fundamental frequency of the wire

1. increases by $1\%$
2. decreases by $1\%$
3. increases by $1.5\%$
4. decreases by $1.5\%$

Q. The fundamental frequency of an open organ pipe is $n$. The pipe is vertically immersed in water such that half of its length is submerged. The fundamental frequency of air column in this position will be

1. $n/3$
2. $n/2$
3. $n$
4. $2n$

Q. Four wires of identical lengths, diameters and materials are stretched on a sonometer wire. The ratio of their tensions is 1 : 4 : 9 : 16. then, the ratio of their fundamental frequencies is

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

Q. A potentiometer wire of length 10 m is connected in series with a battery. The emf of a call balances against 250 cm length of wire. If length of potentiometer wire is increased by 1 m, then new balancing length of wire will be:

1. 2.50 m
2. 2.25 m
3. 2.00 m
4. 2.75 m

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 ?