# String Fixed at Both Ends

## Trending Questions

**Q.**

What happens to frequency when the mass is doubled?

**Q.**

A cylindrical tube open at both ends has a fundamental frequency$f$ in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now

$\frac{f}{2}$

$f$

$\frac{3f}{4}$

$2f$

**Q.**

A pipe closed at one end produces a fundamental note of $412Hz$. It is cut into two pieces of equal length. The fundamental frequencies produced in the two pieces are

$206Hz,412Hz$

$824Hz,1648Hz$

$412Hz,824Hz$

$206Hz,824Hz$

**Q.**The fundamental frequency of a sonometer wire increases by 6 Hz if the tension in the wire is increased by 44%, keeping the length constant. What is the change in the fundamental frequency of the wire when the length is increased by 20%, keeping the original tension in the wire constant.

- 5 Hz
- 10 Hz
- 2.5 Hz
- 7.5 Hz

**Q.**Two strings A and B made of same material, have lengths lA and lB and are connected to two other comparitively denser medium strings having masses MA and MB, the upper ends being supported by rigid supports. If fA and fB are their fundamental frequencies of their vibrations, then fA:fB is

- MAlAMBlB
- lAlB√MAMB
- MAMB√lAlB
- None of these

**Q.**A standing wave is created on a string fixed at both ends, of length 120 cm and it is vibrating in 6th harmonic. Maximum possible amplitude of any particle is 10 cm and maximum possible velocity will be 10 cm/s. Which of the following statement(s) is/are correct?

- Angular wave number (k) of the wave will be π20 cm−1.
- Angular wave number (k) of the wave will be π10 cm−1.
- Time period of any particles SHM will be 4π sec.
- Time period of any particles SHM will be 2π sec.

**Q.**A sonometer wire resonates with a given tuning fork, forming standing waves with five antinodes between the two bridges when a mass of 9 kg is suspended from the wire. When a mass of M kg is suspended from the wire, the same tuning fork causes the wire to form three antinodes for the same positions of the bridges. What is the value of M?

- 25 kg
- 5 kg
- 12.5 kg
- 125 kg

**Q.**A wire of length 2L, is made by joining two wires A and B made of the same material having same length but different radii r and 2r. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire A is p and that in B is q, then the ratio p:q is:

- 3:5
- 1:2
- 4:9
- 1:4

**Q.**Assertion: If a stretched wire fixed at both ends is vibrating in its second overtone mode, then total number of nodes and antinodes are four each.

Reason: If a stretched wire fixed at both ends is vibrating, number of antinodes are equal to number of loops.

You are required to choose correct one of the following

- Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
- Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
- Assertion is true but Reason is false.
- Assertion is false but Reason is true.

**Q.**

A piano wire weighing $6g$and having a length of $90cm$ emits a fundamental frequency corresponding to the “Middle C” $(\nu =261.63Hz)$. Find the tension in the wire.

**Q.**The vibrations of a string of length 20 cm fixed at both ends are represented by the equation y=2sin(πx5)cos(12πt), where x and y are in cm and t in sec. How many nodes are located along the string?

- 3
- 4
- 5
- 6

**Q.**In a stationary wave

- strain is maximum at nodes.
- strain is minimum at nodes.
- strain is maximum at antinodes.
- amplitude is zero at all points.

**Q.**A wire of density 9×10−3 kg cm−3 is stretched between two clamps 1 m apart. The resulting strain in the wire is 4.9×10−4. The lowest frequency of the transverse vibrations in the wire (in Hz) is

(Young's modulus of wire Y=9×1010 Nm−2)

**Q.**A wire having a linear mass density 5×10−3 kg/m is stretched between two rigid supports with a tension of 450 N. The wire resonates at a frequency of 420 Hz. The next higher frequency at which the same wire resonates is 490 Hz. The length of the wire will be

- 4 m
- 2 m
- 8 m
- 3 m

**Q.**The length of a sonometer wire is 1.21 m. It is divided into three segments. What should be the lengths of the three segments for their fundamental frequencies to be in the ratio 1:2:3?

- 0.66 m, 0.33 m, 0.22 m
- 0.72 m, 0.30 m, 0.18 m
- 0.56 m, 0.44 m, 0.21 m
- 0.82 m, 0.18 m, 0.21 m

**Q.**A string fixed at both ends has consecutive standing wave modes for which the distances between adjacent nodes are 18 cm and 16 cm respectively. The minimum possible length of the string is:

- 144 cm
- 152 cm
- 176 cm
- 200 cm

**Q.**The frequency of a sonometer wire is 300 Hz. The frequency becomes half when the mass producing the tension in the wire is completely immersed in water and on immersing the mass in a different liquid, the frequency become one-third. The relative density of the liquid is

**Q.**Two vibrating strings of same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension and vibrate in their fundamental modes with frequencies f1 and f2 respectively. The ratio of f1f2 is given by (strings are fixed at both ends)

- 2
- 4
- 8
- 1

**Q.**In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to (34)th of the original length (mass per unit length remains same) and the tension is changed. The factor by which the tension is to be increased is

- 38
- 23
- 89
- 94

**Q.**

A tuning fork of frequency 480 Hz is used to vibrate a sono-meter wire having natural frequency 240 Hz. The wire will vibrate with a frequency of

240 Hz

480 Hz

720 Hz

will not vibrate

**Q.**

Three resonant frequencies of a string are 90, 150 and 210 Hz.

(i) Find the highest possible fundamental frequency of vibration of this string

(ii) Which harmonics of the fundamental are the given frequencies?

(iii) Which overtones are these frequencies?

30Hz, harmonics - 3rd, 5th, 7th, overtones - 2nd, 4th, 6th

60 Hz, harmonics - 3rd, 5th, 7th, overtones - 2nd, 4th, 6th

30 Hz, harmonics - 2nd, 4th, 6th, overtones, 3rd, 5th, 7th

None of these

**Q.**A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416 Hz. If the length is doubled keeping other things same, the string will

- vibrate with a frequency of 416 Hz
- vibrate with a frequency of 208 Hz
- vibrate with a frequency of 832 Hz
- stop vibrating.

**Q.**The length of the wire shown in figure between the pulley and fixed support is 1.5 m and mass is 12.0 g. The frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulley and the fixed support, is: [Assume the pulley acts as a fixed support and consider g=10 m/s2]

- 10 Hz
- 30 Hz
- 100 Hz
- 70 Hz

**Q.**A steel wire of length 116 cm is connected to an aluminum wire of length 150 cm and stretched between two fixed supports. The tension produced is 52 N. The cross-section of each wire is 2 mm2. If a transverse wave is set up in the wire, find the lowest frequency for which standing waves with a node at the joint are produced. (density of aluminum (ρal)=2.6 g/cm3 and density of steel (ρs)=7.8 g/cm3).

- 50 Hz
- 100 Hz
- 150 Hz
- 200 Hz

**Q.**A string of length 2 m is fixed at both ends. If the speed of transverse wave on the string be 500 m/s, then what will be the frequency of vibration of string in its fifth harmonic and corresponding wavelength of the wave?

- 125 Hz, 0.5 m
- 625 Hz, 0.8 m
- 500 Hz, 1.25 m
- 250 Hz, 0.5 m

**Q.**In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to (34)th of the original length (mass per unit length remains same) and the tension is changed. The factor by which the tension is to be increased is

- 38
- 23
- 89
- 94

**Q.**A string of length L vibrates with a frequency of 7.5 Hz to form a standing wave with three antinodes as shown below.

What is the oscillating frequency of this string, if it produces the standing wave pattern shown below?

- 10 Hz
- 7.5 Hz
- 2.5 Hz
- 15 Hz

**Q.**A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5×10−2 kg and its linear density is 4.0×10−2 kg m−1. The tension in the string is approximately -

- 300.47N
- 425.25 N
- 247.27 N
- 500 N

**Q.**

The fundamental frequency of a segment of wire vibrating is $450Hz$ and it is under a tension of $9kg\u2013wt$. Then, the tension at which the fundamental frequency of the same wire becomes$900Hz$ is

$36kg-wt$

$27kg-wt$

$18kg-wt$

$72kg-wt$

**Q.**The fundamental frequency of a sonometer wire increases by 6 Hz, if its tension is increased by 44%, keeping the length constant. Find the change in the fundamental frequency of the sonometer wire when the length of the wire is increased by 40%, keeping the original tension in the wire constant.

- 8.6 Hz
- 21.4 Hz
- 51.4 Hz
- 17.2 Hz