Advertisements
Advertisements
प्रश्न
A small source of sound S of frequency 500 Hz is attached to the end of a light string and is whirled in a vertical circle of radius 1.6 m. The string just remains tight when the source is at the highest point. (a) An observer is located in the same vertical plane at a large distance and at the same height as the centre of the circle. The speed of sound in air = 330 m s−1 and g = 10 m s−2. Find the maximum frequency heard by the observer. (b) An observer is situated at a large distance vertically above the centre of the circle. Find the frequency heard by the observer corresponding to the sound emitted by the source when it is at the same height as the centre.
Advertisements
उत्तर
Given:
Frequency of sound emitted by the source \[f_0\] = 500 Hz
Velocity of sound in air v = 330 ms-1
Radius of the circle r = 1.6 m
Frequency of sound heard by the observer v, = ?
(a)
Velocity of source at highest point of the circle A is given by :
\[v_s = \sqrt{rg}\]=\[\sqrt{10 \times 1 . 6} = 4 \text { m/s }\]
Velocity of sound at C is \[v_c = \sqrt{5rg} = \sqrt{5 \times 1 . 6 \times 10} = 8 . 9 \text { m/s }\]
The frequency of sound heard by the observer when the source is at point C :
\[f_C = \frac{v}{v - v_s} \times f_0\]
Substituting the values, we get :
\[f_C = \frac{330}{330 - 8 . 9} \times 500\]
\[ \Rightarrow f_C = 513 . 85 \text { Hz } \approx 514 \text { Hz }\]
Frequency of sound observed by the observer when the source is at point A :
\[f_A = \frac{v}{v + v_s} \times n_0 \]
\[ = \frac{300}{300 + 4} \times 500 = 494 \text { Hz }\]
Therefore, maximum frequency heard by the observer is 514 Hz.
(b) Velocity at B is given by :
\[v_B = \sqrt{3rg} = \sqrt{3 \times 1 . 6 \times 10} = 6 . 92 \text { m/s }\]
Frequency at B \[\left( f_B \right)\] will be :
\[f_B = \frac{v}{v + v_s} \times f_0 \]
\[ = \frac{330}{330 + 6 . 92} \times 500 = 490 \text { Hz }\]
Frequency at D \[\left( f_D \right)\] will be :
\[f_D = \frac{v}{v - v_s} \times f_0 \]
\[ = \frac{330}{330 - 6 . 92} \times 500 = 511 \text{ Hz }\]
APPEARS IN
संबंधित प्रश्न
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 voice of a person, who has inhaled helium, has a remarkably high pitch. Explain on the basis of resonant vibration of vocal cord filled with air and with helium.
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
When sound wave is refracted from air to water, which of the following will remain unchanged?
An electrically maintained tuning fork vibrates with constant frequency and constant amplitude. If the temperature of the surrounding air increases but pressure remains constant, the produced will have
(a) larger wavelength
(b) larger frequency
(c) larger velocity
(d) larger time period.
The fundamental frequency of a vibrating organ pipe is 200 Hz.
(a) The first overtone is 400 Hz.
(b) The first overtone may be 400 Hz.
(c) The first overtone may be 600 Hz.
(d) 600 Hz is an overtone.
A listener is at rest with respect to the source of sound. A wind starts blowing along the line joining the source and the observer. Which of the following quantities do not change?
(a) Frequency
(b) Velocity of sound
(c) Wavelength
(d) Time period
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.
If the intensity of sound is doubled, by how many decibels does the sound level increase?
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.
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.
In a standing wave pattern in a vibrating air column, nodes are formed at a distance of 4.0 cm. If the speed of sound in air is 328 m s−1, what is the frequency of the source?
A sound source, fixed at the origin, is continuously emitting sound at a frequency of 660 Hz. The sound travels in air at a speed of 330 m s−1. A listener is moving along the lien x= 336 m at a constant speed of 26 m s−1. Find the frequency of the sound as observed by the listener when he is (a) at y = − 140 m, (b) at y = 0 and (c) at y = 140 m.
A source of sound emitting a 1200 Hz note travels along a straight line at a speed of 170 m s−1. A detector is placed at a distance 200 m from the line of motion of the source. (a) Find the frequency of sound receive by the detector at the instant when the source gets closest to it. (b) Find the distance between the source and the detector at the instant in detects the frequency 1200 Hz. Velocity of sound in air = 340 m s−1.
With propagation of longitudinal waves through a medium, the quantity transmitted is ______.
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.
