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
Can you hear your own words if you are standing in a perfect vacuum? Can you hear your friend in the same conditions?
Two loudspeakers are arranged facing each other at some distance. Will a person standing behind one of the loudspeakers clearly hear the sound of the other loudspeaker or the clarity will be seriously damaged because of the 'collision' of the two sounds in between?
Two tuning forks vibrate with the same amplitude but the frequency of the first is double the frequency of the second. Which fork produces more intense sound in air?
Two sound waves move in the same direction in the same medium. The pressure amplitudes of the waves are equal but the wavelength of the first wave is double the second. Let the average power transmitted across a cross section by the first wave be P1 and that by the second wave be P2. Then
When you speak to your friend, which of the following parameters have a unique value in the sound produced?
Find the minimum and maximum wavelengths of sound in water that is in the audible range (20−20000 Hz) for an average human ear. Speed of sound in water = 1450 m s−1.
A sound wave frequency 100 Hz is travelling in air. The speed of sound in air is 350 m s−1. (a) By how much is the phase changed at a given point in 2.5 ms? (b) What is the phase difference at a given instant between two points separated by a distance of 10.0 cm along the direction of propagation?
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.
A uniform horizontal rod of length 40 cm and mass 1⋅2 kg is supported by two identical wires as shown in figure. Where should a mass of 4⋅8 kg be placed on the rod so that the same tuning fork may excite the wire on left into its fundamental vibrations and that on right into its first overtone? Take g = 10 m s−2.
Three sources of sound S1, S2 and S3 of equal intensity are placed in a straight line with S1S2 = S2S3. At a point P, far away from the sources, the wave coming from S2 is 120° ahead in phase of that from S1. Also, the wave coming from S3 is 120° ahead of that from S2. What would be the resultant intensity of sound at P?
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?
A piano wire A vibrates at a fundamental frequency of 600 Hz. A second identical wire Bproduces 6 beats per second with it when the tension in A is slightly increased. Find the the ratio of the tension in A to the tension in B.
A small source of sound oscillates in simple harmonic motion with an amplitude of 17 cm. A detector is placed along the line of motion of the source. The source emits a sound of frequency 800 Hz which travels at a speed of 340 m s−1. If the width of the frequency band detected by the detector is 8 Hz, find the time period of the source.
A boy riding on his bike is going towards east at a speed of 4√2 m s−1. At a certain point he produces a sound pulse of frequency 1650 Hz that travels in air at a speed of 334 m s−1. A second boy stands on the ground 45° south of east from his. Find the frequency of the pulse as received by the second boy.
A transverse wave is represented by y = 2sin (ωt - kx) cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be ______.
