Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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 we clap our hands, the sound produced is best described by Here p denotes the change in pressure from the equilibrium value.
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
Two sound waves move in the same direction in the same medium. The pressure amplitudes of the waves are equal but the wavelength of the first wave is double the second. Let the average power transmitted across a cross section by the first wave be P1 and that by the second wave be P2. Then
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
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.
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.
A sound wave frequency 100 Hz is travelling in air. The speed of sound in air is 350 m s−1. (a) By how much is the phase changed at a given point in 2.5 ms? (b) What is the phase difference at a given instant between two points separated by a distance of 10.0 cm along the direction of propagation?
At what temperature will the speed of sound be double of its value at 0°C?
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?
A string, fixed at both ends, vibrates in a resonant mode with a separation of 2⋅0 cm between the consecutive nodes. For the next higher resonant frequency, this separation is reduced to 1⋅6 cm. Find the length of the string.
A string of length L fixed at both ends vibrates in its fundamental mode at a frequency ν and a maximum amplitude A. (a)
- Find the wavelength and the wave number k.
- Take the origin at one end of the string and the X-axis along the string. Take the Y-axis along the direction of the displacement. Take t = 0 at the instant when the middle point of the string passes through its mean position and is going towards the positive y-direction. Write the equation describing the standing wave.
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 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?
A tuning fork of frequency 256 Hz produces 4 beats per second with a wire of length 25 cm vibrating in its fundamental mode. The beat frequency decreases when the length is slightly shortened. What could be the minimum length by which the wire we shortened so that it produces no beats with the tuning fork?
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 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.
With propagation of longitudinal waves through a medium, the quantity transmitted is ______.
Which of the following statements are true for wave motion?
