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
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
Can you hear your own words if you are standing in a perfect vacuum? Can you hear your friend in the same conditions?
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.
A tuning fork sends sound waves in air. If the temperature of the air increases, which of the following parameters will change?
When sound wave is refracted from air to water, which of the following will remain unchanged?
A small source of sounds moves on a circle as shown in figure and an observer is sitting at O. Let \[v_1, v_2, v_3\] be the frequencies heard when the source is at A, B and C respectively.
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.
A man stands before a large wall at a distance of 50.0 m and claps his hands at regular intervals. Initially, the interval is large. He gradually reduces the interval and fixes it at a value when the echo of a clap merges every 3 seconds, find the velocity of sound in air.
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?
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?
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 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 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.
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.
With propagation of longitudinal waves through a medium, the quantity transmitted is ______.
Which of the following statements are true for wave motion?
Equation of a plane progressive wave is given by `y = 0.6 sin 2π (t - x/2)`. On reflection from a denser medium its amplitude becomes 2/3 of the amplitude of the incident wave. The equation of the reflected wave 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.
