Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given:
Frequency of sound emitted by the source \[n_0\]= 660 Hz
Velocity of sound in air v = 330 `\text { ms}^\(-)`1
Velocity of observer \[v_0\]= 26 ms−1
Frequency of sound heard by observer n = ?
(a) At y = 140 m:
Frequency of sound heard by the listener, when the source is fixed but the listener is moving towards the source:
\[n = \frac{v + v_0}{v} n_0 \]
Here ,
\[v_0 = v_0 \cos\theta\]
On substituting the values, we get:
\[n = \frac{v + v_0 \cos\theta}{v} n_0 \]
\[ = \frac{330 + 26 \times \frac{140}{364}}{330} \times 660\]
\[ = 340 \times 2 = 680 \text{ Hz }\]
(b) When the observer is at y = 0, the velocity of the observer with respect to the source is zero.
Therefore, he will hear at a frequency of 660 Hz.
(c) When the observer is at y = 140 m:
\[n = \frac{v - v_0}{v} \times n_0 \]
Here,
\[v_0 = v_0 \cos\theta\]
On substituting the values, we get:
\[n = \frac{330 - \frac{26 \times 140}{364}}{330} \times 660\]
\[n = \frac{330 - 10}{330} \times 660 = 640 \text { Hz }\]
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
A wave is represented by an equation \[y = c_1 \sin \left( c_2 x + c_3 t \right)\] In which direction is the wave going? Assume that \[c_1 , c_2\] \[c_3\] are all positive.
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.
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?
A tuning fork of frequency 512 Hz is vibrated with a sonometer wire and 6 beats per second are heard. The beat frequency reduces if the tension in the string is slightly increased. The original frequency of vibration of the string is
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.
Two point sources of sound are kept at a separation of 10 cm. They vibrate in phase to produce waves of wavelength 5.0 cm. What would be the phase difference between the two waves arriving at a point 20 cm from one source (a) on the line joining the sources and (b) on the perpendicular bisector of the line joining the sources?
A sources of sound operates at 2.0 kHz, 20 W emitting sound uniformly in all directions. The speed of sound in air is 340 m s−1 and the density of air is 1.2 kg m −3. (a) What is the intensity at a distance of 6.0 m from the source? (b) What will be the pressure amplitude at this point? (c) What will be the displacement amplitude at this point?
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?
If the intensity of sound is doubled, by how many decibels does the sound level increase?
Sound with intensity larger than 120 dB appears pain full to a person. A small speaker delivers 2.0 W of audio output. How close can the person get to the speaker without hurting his ears?
If the sound level in a room is increased from 50 dB to 60 dB, by what factor is the pressure amplitude increased?
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.
The two sources of sound, S1 and S2, emitting waves of equal wavelength 20.0 cm, are placed with a separation of 20.0 cm between them. A detector can be moved on a line parallel to S1 S2 and at a distance of 20.0 cm from it. Initially, the detector is equidistant from the two sources. Assuming that the waves emitted by the sources are in detector should be shifted to detect a minimum of sound.
Two speakers S1 and S2, driven by the same amplifier, are placed at y = 1.0 m and y = −1.0 m(See figure). The speakers vibrate in phase at 600 Hz. A man stands at a point on the X-axis at a very large distance from the origin and starts moving parallel to the Y-axis. The speed of sound in air is 330 m s−1. (a) At what angle θ will the intensity of sound drop to a minimum for the first time? (b) At what angle will he hear a maximum of sound intensity for the first time? (c) If he continues to walk along the line, how many more can he hear?
The first overtone frequency of a closed organ pipe P1 is equal to the fundamental frequency of a open organ pipe P2. If the length of the pipe P1 is 30 cm, what will be the length of P2?
Consider the situation shown in the figure.The wire which has a mass of 4.00 g oscillates in its second harmonic and sets the air column in the tube into vibrations in its fundamental mode. Assuming that the speed of sound in air is 340 m s−1, find the tension in the wire.
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 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.
