Advertisements
Advertisements
प्रश्न
A string, fixed at both ends, vibrates in a resonant mode 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.
Advertisements
उत्तर
Given:
Separation between two consecutive nodes when the string vibrates in resonant mode = 2.0 cm
Let there be 'n' loops and
\[\lambda\] be the wavelength.
∴
\[\lambda\] = \[2 \times Separation between the consecutive nodes\]
\[\lambda_1 = 2 \times 2 = 4 \text{ cm }\]
\[\lambda_2 = 2 \times 1 . 6 = 3 . 2 cm\]
Length of the wire is L.
In the first case:
\[L = \left( \frac{n \lambda_1}{2} \right)\]
In the second case:
\[L = \left( n + 1 \right)\frac{\lambda_2}{2}\]
\[ \Rightarrow \frac{n \lambda_1}{2} = \left( n + 1 \right) \frac{\lambda_2}{2}\]
\[ \Rightarrow n \times 4 = \left( n + 1 \right)\left( 3 . 2 \right)\]
\[ \Rightarrow 4n - 3 . 2n = 3 . 2\]
\[ \Rightarrow 0 . 8 n = 3 . 2\]
\[ \Rightarrow n = 4
\text{ ∴ length of the string,}\]
\[L = \frac{\left( n \lambda_1 \right)}{2} = \frac{\left( 4 \times 4 \right)}{2} = 8 \text{ cm }\]
APPEARS IN
संबंधित प्रश्न
Explain what is Doppler effect in sound
The wavelengths of two sound waves in air are `81/173`m and `81/170`m. They produce 10 beats per second. Calculate the velocity of sound in air
The equation \[y = A \sin^2 \left( kx - \omega t \right)\]
represents a wave motion with
The bulk modulus and the density of water are greater than those of air. With this much of information, we can say that velocity of sound in air
A small source of sounds moves on a circle as shown in figure and an observer is sitting at O. Let \[v_1, v_2, v_3\] be the frequencies heard when the source is at A, B and C respectively.
When you speak to your friend, which of the following parameters have a unique value in the sound produced?
The equation of a travelling sound wave is y = 6.0 sin (600 t − 1.8 x) where y is measured in 10−5 m, t in second and x in metre. (a) Find the ratio of the displacement amplitude of the particles to the wavelength of the wave. (b) Find the ratio of the velocity amplitude of the particles to the wave speed.
Calculate the bulk modulus of air from the following data about a sound wave of wavelength 35 cm travelling in air. The pressure at a point varies between (1.0 × 105 ± 14) Pa and the particles of the air vibrate in simple harmonic motion of amplitude 5.5 × 10−6 m.
The sound level at a point 5.0 m away from a point source is 40 dB. What will be the level at a point 50 m away from the source?
A source of sound S and detector D are placed at some distance from one another. a big cardboard is placed near hte detector and perpendicular to the line SD as shown in figure. It is gradually moved away and it is found that the intensity changes from a maximum to a minimum as the board is moved through a distance of 20 cm. Find the frequency of the sound emitted. Velocity of sound in air is 336 m s−1.
A string of length L fixed at both ends vibrates in its fundamental mode at a frequency ν and a maximum amplitude A. (a)
- Find the wavelength and the wave number k.
- Take the origin at one end of the string and the X-axis along the string. Take the Y-axis along the direction of the displacement. Take t = 0 at the instant when the middle point of the string passes through its mean position and is going towards the positive y-direction. Write the equation describing the standing wave.
Figure shown two coherent sources S1 and S2 which emit sound of wavelength λ in phase. The separation between the sources is 3λ. A circular wire of large radius is placed in such way that S1,S2 is at the centre of the wire. Find the angular positions θ on the wire for which constructive interference takes place.
A heavy string is tied at one end to a movable support and to a light thread at the other end as shown in following 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?
The separation between a node and the next antinode in a vibrating air column is 25 cm. If the speed of sound in air is 340 m s−1, find the frequency of vibration of the air column.
A tuning fork produces 4 beats per second with another tuning fork of frequency 256 Hz. The first one is now loaded with a little wax and the beat frequency is found to increase to 6 per second. What was the original frequency of the tuning fork?
Show that if the room temperature changes by a small amount from T to T + ∆T, the fundamental frequency of an organ pipe changes from v to v + ∆v, where \[\frac{∆ v}{v} = \frac{1}{2}\frac{∆ T}{T} .\]
A train running at 108 km h−1 towards east whistles at a dominant frequency of 500 Hz. Speed of sound in air is 340 m/s. What frequency will a passenger sitting near the open window hear? (b) What frequency will a person standing near the track hear whom the train has just passed? (c) A wind starts blowing towards east at a speed of 36 km h−1. Calculate the frequencies heard by the passenger in the train and by the person standing near the track.
During propagation of a plane progressive mechanical wave ______.
- all the particles are vibrating in the same phase.
- amplitude of all the particles is equal.
- particles of the medium executes S.H.M.
- wave velocity depends upon the nature of the medium.
The speed of a wave in a string is 20 m/s and the frequency is 50 Hz. The phase difference between two points on the string 10 cm apart will be ______.
