Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Given:
Velocity of sound in air v = 340 ms−1
Power of the source P = 20 W
Frequency of the source f = 2,000 Hz
Density of air ρ = 1.2 kgm −3
(a) Distance of the source r = 6.0 m
Intensity is given by:
\[I = \frac{P}{A}\]
where A is the area.
\[\Rightarrow I = \frac{20}{4\pi r^2} = \frac{20}{4 \times \pi \times 6^2} \left( \because r = 6 m \right)\]
\[ \Rightarrow I = 44 \text { mw/ m }^2\]
(b) As we know,
\[I = \frac{p_0^2}{2\rho v} . \]
\[ \Rightarrow P_0 = \sqrt{I \times 2\rho v}\]
\[ \Rightarrow P_0 = \sqrt{2 \times 1 . 2 \times 340 \times 44 \times {10}^{- 3}}\]
\[ \Rightarrow P_0 = 6 . 0 \text { Pa } \text { or } \text { N/ m }^2\]
(c) As we know, I = 2π2S02v2ρV.
S0 is the displacement amplitude.
\[\Rightarrow S_0 = \sqrt{\frac{I}{2 \pi^2 v^2 \rho V}}\]
On applying the respective values, we get:
S0 = 1.2 × 10−6 m
APPEARS IN
संबंधित प्रश्न
What is the smallest positive phase constant which is equivalent to 7⋅5 π?
If you are walking on the moon, can you hear the sound of stones cracking behind you? Can you hear the sound of your own footsteps?
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.
When you speak to your friend, which of the following parameters have a unique value in the sound produced?
A person can hear sound waves in the frequency range 20 Hz to 20 kHz. Find the minimum and the maximum wavelengths of sound that is audible to the person. The speed of sound is 360 m s−1.
The absolute temperature of air in a region linearly increases from T1 to T2 in a space of width d. Find the time taken by a sound wave to go through the region in terms of T1, T2, d and the speed v of sound at 273 K. Evaluate this time for T1 = 280 K, T2 = 310 K, d = 33 m and v = 330 m s−1.
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 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?
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?
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?
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?
A cylindrical tube, open at both ends, has a fundamental frequency v. The tube is dipped vertically in water so that half of its length is inside the water. The new fundamental frequency is
With propagation of longitudinal waves through a medium, the quantity transmitted is ______.
Which of the following statements are true for wave motion?
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.
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 ______.
