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
A string clamped at both ends vibrates in its fundamental mode. Is there any position (except the ends) on the string which can be touched without disturbing the motion? What if the string vibrates in its first overtone?
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?
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
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.
Sound waves from a loudspeaker spread nearly uniformly in all directions if the wavelength of the sound is much larger than the diameter of the loudspeaker. (a)Calculate the frequency for which the wavelength of sound in air is ten times the diameter of the speaker if the diameter is 20 cm. (b) Sound is essentially transmitted in the forward direction if the wavelength is much shorter than the diameter of the speaker. Calculate the frequency at which the wavelength of the sound is one tenth of the diameter of the speaker described above. Take the speed of sound to be 340 m/s.
The intensity of sound from a point source is 1.0 × 10−8 W m−2 at a distance of 5.0 m from the source. What will be the intensity at a distance of 25 m from the source?
If the intensity of sound is doubled, by how many decibels does the sound level increase?
A particular guitar wire is 30⋅0 cm long and vibrates at a frequency of 196 Hz when no finger is placed on it. The next higher notes on the scale are 220 Hz, 247 Hz, 262 Hz and 294 Hz. How far from the end of the string must the finger be placed to play these notes?
The noise level in a classroom in absence of the teacher is 50 dB when 50 students are present. Assuming that on the average each student output same sound energy per second, what will be the noise level if the number of students is increased to 100?
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.
A traffic policeman standing on a road sounds a whistle emitting the main frequency of 2.00 kHz. What could be the apparent frequency heard by a scooter-driver approaching the policeman at a speed of 36.0 km h−1? Speed of sound in air = 340 m s−1.
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 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.
A boy riding on a bicycle going at 12 km h−1 towards a vertical wall whistles at his dog on the ground. If the frequency of the whistle is 1600 Hz and the speed of sound in air is 330 m s−1, find (a) the frequency of the whistle as received by the wall (b) the frequency of the reflected whistle as received by the boy.
A car moves with a speed of 54 km h−1 towards a cliff. The horn of the car emits sound of frequency 400 Hz at a speed of 335 m s−1. (a) Find the wavelength of the sound emitted by the horn in front of the car. (b) Find the wavelength of the wave reflected from the cliff. (c) What frequency does a person sitting in the car hear for the reflected sound wave? (d) How many beats does he hear in 10 seconds between the sound coming directly from the horn and that coming after the reflection?
Figure shows a source of sound moving along X-axis at a speed of 22 m s−1continuously emitting a sound of frequency 2.0 kHz which travels in air at a speed of 330 m s−1. A listener Q stands on the Y-axis at a distance of 330 m from the origin. At t = 0, the sources crosses the origin P. (a) When does the sound emitted from the source at P reach the listener Q? (b) What will be the frequency heard by the listener at this instant? (c) Where will the source be at this instant?
For the propagation of longitudinal waves, the medium must have
- elasticity
- mass
- inertia
- force of cohesion
In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms-1. The third resonance is observed when the air column has a length of ______ cm.
