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H C VERMA PHYSICS BOOK SOLUTIONS SOUND WAVES PART 1

Solved Examples
1.    A wave of wavelength 0.40 cm is produced in air and it travels at a speed of 300 m/s. Will it be audible ?
Sol.    From the relation v = nl, the frequency of the wave is 
       
    This is much above the audible range. It is an ultrasonic wave and will not be audible to humans, but it will be audible to bats.

2.    A sound wave of wavelength to bats 40 cm travels in air. If the difference between the maximum and minimum pressures at a given point is 2.0 × 10–3 N/m2, find the amplitude of vibration of the particles of the medium. The bulk modulus of air is 1.4 × 105 N/m2.
Sol.    The pressure amplitude is 
      

3.    The pressure amplitude in a sound wave from a radio receiver is 2.0 × 10–3 N/m2 and the intensity at a point is 10–6 W/m2. If by turning the “Volume” knob the pressure amplitude is increased to 3 × 10–3 N/m2, evaluate the intensity.
Sol.    The intensity is proportional to the square of the pressure amplitude.
  

4.    If the intensity is increased by a factor of 20, by how many decibels is the level increased.

Sol.    Let the initial intensity by I and the second level be b1. When the intensity is increased to 20 the level increases to b2.
 

5.    Two sound waves, originating from the same source, travel along different paths in air and then meet at a point. If the source vibrates at a frequency of 1.0 kHz and one path is 83 cm longer than the other, what will be the natural of interference ? The speed of sound in air is 332 m/s.

Sol.    The wavelength of sound wave is 
        =  332/103HZ.
    
    As this is an odd multiple of p, the waves interfere destructively.

6.    An air column is constructed by fitting a movable piston in a long cylindrical tube. Longitudinal waves are sent in the tube by a tuning fork of frequency 416 Hz. How far from the open end should the piston be so that the air column in the tube may vibrate in its first overtone? Speed of sound in air is 333 m/s.

Sol.    The piston provides the closed end of the column and an antinode of pressure is formed there. At the open end, a pressure node is formed. In the first overtone there is one more node and an antinode in the column as shown in figure. The length of the tube should then be 3l/4.


                    
    The wavelength is
    

  Thus, the length of the tube is 
           

7.    A tuning fork A of frequency 384 Hz gives 6 beats in 2 seconds when sounded with another tuning fork B. What could be the frequency of B?

Sol.    The frequency of beats is | v1 – v2 |, which is 3 Hz according to the problem. The frequency of the tuning fork B is either 3 Hz more or 3 Hz less than the frequency of A. Thus, it could be either 
381 Hz or 387 Hz.

8.    A sound detector is placed on a railway platform. A train, approaching the platform at a speed of 36 km/h, sounds its whistle. The detector detects 12.0 kHz as the most dominant frequency in the whistle. If the train stops at the platform and sounds the whistle, what would be the most dominant frequency detected ? The speed of sound in air is 340 m/s.

Sol.    Here the observer (detector) is at rest with respect to the medium (air). Suppose the dominant frequency as emitted by the train is v0. When the train is at rest at the platform, the detector will detect the dominant frequency as v0. When this same train was approaching the observer, the frequency detected was,
       
    The speed of the source is 
     

Questions for Short answer
1.    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?
    
2.    Can you hear your own wards if you are standing in a perfect vacuum? Can you hear your friend in the same conditions?

3.    A vertical rod is hit at one end. What kind of wave propagates in the rod is (a) the hit is made vertically (b) the hit is made horizontally?

4.    Two loudspeakers are arranged facing each other at some distance. Will a person standing behind one of the loudspeakers clearly hear the sound of the other loudspeaker or the clarity will be seriously damaged because of the ‘collision’ of the two sounds in between ?

5.    The voice of a person, who have inhaled helium, has a remarkably high pitch. Explain on the basis of resonant vibration of vocal cord filled with air and with helium.

6.    Draw a diagram to show the standing pressure wave and standing displacement wave for the 3rd overtone mode of vibration of an open organ pipe.

7.    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?

8.    In discussing Doppler effect, we use the word “apparent frequency”. Does it mean that the frequency of the sound is still that of the source and it is some physiological phenomenon in the listener’s ear that gives rise to Doppler effect? Think for the observer approaching the source and for the source approaching the observer.

 

Objective - I

 


1.    Consider the following statements about sound passing through a gas.
    (A*) the pressure of the gas at a point oscillates in time    (B) A is correct but B is wrong
    (C) B is correct but A is wrong                (D) Both A and B are wrong
    

2.    When we clap our hands, the sound produced is best described by     
    
    Here p denotes the change in pressure from the equilibrium value.
    
    
3.    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

    (A) is larger than its value in water        (B) is smaller than its value in water
    (C) is equal to its value in water            (D*) cannot be compared with its value in water
   

4.    A tuning fork sends sound waves in air. If the temperature of the air increases, which of the following parameters will change ?
    (A) displacement amplitude            (B) Frequency
    (C*) Wavelength                    (D) time period
    
5.    When sound wave is refracted from air to water, which of the following will remain unchanged?
    (A) wave number    (B) wavelength         (C) wave velocity     (D*) frequency
    
6.    The speed of sound in a medium depends on 
    (A) the elastic property but not on the inertia property 
    (B) the inertia property but not on the elastic property 
    (C*) the elastic property as well as the inertia property
    (D) neither the elastic property nor the inertia property
    

7.  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*) P1 = P2        (B) P1 = 4P2        (C) P2 = 2P1        (D) P2 = 4P1

8.    When two waves with same frequency and constant phase difference interfere,
    tc leku vko`fÙk rFkk fu;r dykUrj okyh nks rjaxsa O;frdj.k djrh gS] rks &
    (A) there is a gain of energy    
    (B) there is a loss of energy  
    (C) the energy is redistributed and the distribution changes with time 
    
    (D*) the energy is redistributed and the distribution remains constant in time
    

9.    An open organ pipe of length L vibrates in its fundamental mode. The pressure variation is maximum 
    (A) at the two ends                                (B*) at the middle of the pipe
    (C) at distance L/4 inside the ends        (D) at distance L/8 inside the ends
    
10.    An organ pipe, open at both ends, contains    
    (A*) longitudinal stationery waves        (B) longitudinal travelling waves    
    (C) transverse stationary waves            (D) transverse travelling waves
    
11.    A cylindrical tube, open at both ends, has a fundamental frequency f. The tube is dipped vertically in water so that half of its length is inside the water. The new fundamental frequency is
    
    (A) f/4            (B) f/2            (C*) f            (D) 2f

12.    The phenomenon of beats can take place 
    (A) for longitudinal wave only                (B) for transverse wave only    
    (C*) for both longitudinal and transverse waves         (D) for sound waves only.
    
13.    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*) 506 Hz        (B) 512 Hz        (C) 518 Hz        (D) 524 Hz
14.    The engine of a train sounds a whistle at frequency f. The frequency heard by a passenger is
    
    (A)  > f        (B)  < f            (C)  =(1 / f)        (D*)  = f

15.    The change in frequency due to Doppler effect does not depend on
    (A) the speed of the source        (B) the speed of the observer
    (C) the frequency of the source        (D*) separation between the source and the observer
    
16.    A small source of sound moves on a circle as shown in fig. and an observer is sitting at O. Let at  f1, f2, f3 be the frequencies heard when the source is at A, B, and C respectively.
    
                    
    (A) f1 > f2 > f3        (B) f1 = f2 > f3        (C) f2 > f3 > f1        (D*)     f1 >f3 > f2

 

Objective - II


1.    When you speak to your friend, which of the following parameters have a unique value in the sound produced?
    (A) Frequency         (B) Wavelength        (C) Amplitude        (D*) Wave velocity
    

2.    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 sound produced will have
    (A*) large wavelength     (B) larger frequency      (C*) larger velocity    (D) larger time period
        
3.    The fundamental frequency of a vibrating organ pipe is 200 Hz.
    (A) The first overtone is 400 Hz.            (B*) The first overtone may be 400 Hz.
    (C*) The first overtone may be 600 Hz        (D*) 600 Hz is an overtone
    
4.    A source of sound moves towards an observer
    (A) The frequency of the source is increased 
    (B) The velocity of sound in the medium is increased
    (C*) The wavelength of sound in the medium towards the observer is decreased
    (D) The amplitude of vibration of the particles is increased
    

5.    A listener is at rest with respect to the source of sound. A wind starts blowing along the line joining the source and the observer. Which of the following quantities do not change?
    (A*) Frequency        (B) Velocity of sound    (C) Wavelength        (D*) Time period
    

Worked Out Examples


1.    An ultrasound signal of frequency 50 kHz is sent vertically into sea water. The signal gets reflected from the ocean bed and returns to the surface 0.80 s after it was emitted. The speed of sound in sea water is 1500 m/s. (a) Find the depth of the sea. (b) What is the wavelength of this signal in water ?
Sol.    (a) Let the depth of the sea be d. The total distance travelled by the signal is 2d. By the question, 
        2d = (1500 m/s) (0.8 s) = 1200 m
    or,    d = 600 m.
    (b)    Using the equation u = vl,
        l =  =  = 3.0 cm.

2.    An aeroplane is going towards east at a speed of 510 km/h at a height of 2000 m. At a certain instant, the sound of the plane heard by a ground observer appears to come from a point vertically about him. Where is the plane at this instant ? Speed of sound in air = 340 m/s.
    
Sol.    The sound reaching the ground observer P, was emitted by the plane when it was at the point Q vertically above his head. The time taken by the sound to reach the observer is 
                
        t =  2000m/340m/s  =(100/17)second
    The distance moved by the plane during this period is 
        d = (510 km/h{100/17}

           = (3x106 ) /3600m = 833 m.
    Thus, the plane will be 833 m ahead of the observer on its line of motion when he hears the sound coming vertically to him.

3.    The equation of a sound wave in air is given by 
        p = (0.01 N/m2) sin [(1000 s–1) t – (3.0 m–1) x ]
    (a)    Find the frequency, wavelength and the speed of sound wave in air. 
    (b)     If the equilibrium pressure of air is 1.0 × 105 N/m2, what are the maximum and minimum         pressures at a point as the wave passes through that point?
Sol.    (a)    Comparing with the standard form of a travelling wave
          
        Also from the same comparison, w/v = 3.0 m–1.
        or,   
        The wavelength is
    

(b)    The pressure amplitude is p0 = 0.01 N/m2. Hence, the maximum and minimum pressures at a point in the wave motion will be (1.01 × 105 ± 0.01) N/m2.

4.    A sound wave of frequency 10 kHz is travelling in air with a speed of 340 m/s. Find the minimum separation between two points where the phase difference is 60°.
Sol.  The wavelength of the wave is     
      
    The wave number is
    The phase of the wave is (kx – wt). At any given instant, the phase difference between two points at a separation d is kd. If this phase difference is 60° i.e., pie/3 radian ;
        

5.    On a winter day sound travels 336 metres in one second. Find the atmospheric temperature. Speed of sound at 0°C = 332 m/s.
Sol.    The speed of sound is proportional to the square root of the absolute temperature.
    The speed of sound at 0°C or 273 K is 332 m/s. If the atmospheric temperature is T,
        

6.    The constant g for oxygen as well as for hydrogen is 1.40. If the second of sound in oxygen is 470 m/sm, what will be the speed in hydrogen at the same temperature and pressure?
Sol.    The speed of sound in a gas is given by. At STP, 22.4 litres of oxygen has a mass of 32 g whereas the same volume of hydrogen has a mass of 2 g. Thus, the density of oxygen is 16 times the density of hydrogen at the same temperature and pressure. As g is same for both the gases,
          

7.    A microphone of cross-sectional area 0.80 cm2 is placed in front of a small speaker emitting 3.0 W of sound output. If the distance between the microphone and the speaker is 2.0 m, how much energy falls on the microphone in 5.0 s ?
Sol.    The energy emitted by the speaker in one second is 3.0 J. Let us consider a sphere of radius 2.0 m centred at the speaker. The energy 3.0 J falls normally on the total surface of this sphere in one second. The energy falling on the area 0.8 cm2 of the microphone in one second
      

 

 

H C VERMA PHYSICS BOOK SOLUTIONS SOUND WAVES PART 1

H C VERMA PHYSICS BOOK SOLUTIONS SOUND WAVES PART 2

H C VERMA PHYSICS BOOK SOLUTIONS SOUND WAVES PART 3



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