String Fixed at Both Ends

Q. The frequency of a sonometer wire is $300\text{Hz}$. 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 (upto 2 decimals )

Q.

A string, fixed at both ends, vibrates in a resonant node with a separation of 2.0 cm between the consecutive nodes. For the next higher resonant frequency, this separation is reduced to 1.6 cm. find the length of the string.

1. 18 cm

2. 8 cm

3. cannot be determined

4. 10 cm

Q. A wire of length 2.00 m fixed at both the ends is stretched to a tension of 160 N. if the fundamental frequency of vibration is 100 Hz, find its linear mass density.

1. 1 kg m^-1

2. 10^-3gm^-1

3. 1 gm^-1

4. 10 kgm^-1

Q.

The equation of a standing wave, produced on a string fixed at both ends, is $y=\left(0.4cm\right)sin\left[\right(0.314c{m}^{-1}\left)x\right]cos\left[\right(600\pi s^{-1}\left)t\right]$

What could be the smallest length of the string?

1. 20 cm

2. 10 cm

3. 15 cm

4. None of these

Q.

A 2 m-long string fixed at both ends is set into vibrations in its first overtone. The wave speed on the string is $200m{s}^{-1}$ and the amplitude is 0.5 cm. Write the equation giving the displacement of different points as a function of time. Choose the X-axis along the string with the origin at one end and t = 0 at the instant when the point x = 50 cm has reached its maximum displacement.

1. sin (πx) cos (200π t)

2. sin (2πx) cos (200π t)

3. sin (πx) cos (400π t)

4. sin (2πx) cos (400π t)

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

1. vibrate with a frequency of 208 Hz

2. vibrate with a frequency of 832 Hz

3. stop vibrating.

4. vibrate with a frequency of 416 Hz

Q.

A stone is hung in air from a wire which is stretched over a sonometer. The bridges of the sonometer are L cm apart when the wire is in unison with a tuning fork of frequency n. When the stone is completely immersed in water, the length between the bridges is l cm for re-establishing unison, the specific gravity of the material of the stone is

1. $\frac{L^2-l^2}{2L^2}$

2. 

3. 

4. 

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?

1. 30Hz, harmonics - 3rd, 5th, 7th, overtimes - 2nd, 4th, 6th

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

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

4. None of these

Q.

A sono-meter wire supports a 4 kg load and vibrates in fundamental node with a tuning fork of frequency 416 Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental node, the load should be changed to

1. 1 kg

2. 16 kg

3. 2 kg

4. 8 kg

Q.

A heavy string is tied at one end to a movable support and to a light thread at the other end as shown in figure. The thread goes over a fixed pulley and supports a weight to produce a tension. The lowest frequency with which the heavy string resonates is 120 Hz. If the movable support is pushed to the right by 10 cm so that the joint is placed on the pulley, what will be the minimum frequency at which the heavy string can resonate?

1. 120 Hz

2. 240 Hz

3. 360 Hz

4. None of these