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Sound Waves â?– Illustrative Examples 1) What is the wavelength of radiowave of frequency 530 MHz ? (speed of radio waves in air
)
Data :
(Ans. :
)
2) A turning fork has frequency 288 Hz. Find the number of vibrations of turning fork when the sound from turning fork reaches 330 m in air. Velocity of sound in air is 330 m/s. Data : n = 288 Hz v = 330 m/s Distance travelled by wave S = 330 m No. of vibrations of turning fork N = ? (Ans. :
)
3) The speed of sound in air is 330 m/s and that in glass is 220 m/s. Compare the wavelengths of sound waves in the two media. Data :
(Ans. :
)
4) At what temperature the speed of sound in air will be double than its speed at N.T.P.? Data :
(Ans. : 5) Calculate the speed of sound in air at N.T.P. if the density of air at N.T.P. is 1.29 kg/m3 and
for air is 1.4
Data :
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)
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(Ans. :
)
6) The turning forks emit sound notes differing in wavelength by 30 cm in air. If the frequencies of forks are 100 Hz and 110 Hz respectively, calculate the velocity of sound in air. Data :
(Ans. :
)
❖ Theory Questions 1)
Define wave motion. State the properties of medium for propogation of wave.
2)
State the characteristics of a progressive wave.
3)
What are transverse waves? State their characteristics.
4)
What are longitudinal waves? State their characteristics.
5)
Define the terms wavelength and frequency of a wave. Derive the relation between wave speed, wavelength and frequency.
6)
“Wave motion is a doubly periodic phenomenon”. Explain.
7)
Distinguish between transverse waves and longitudinal waves.
8)
Explain the formation of sound waves in air.
9)
Give the Newton's formula for the velocity of sound in air and state its assumptions.
10) Explain Laplace's correction to the Newton’s formula for the velocity of sound in air. 11) Discuss the effect of temperature, humidity and pressure on the velocity of sound in air. Obtain the necessary relations. 12) Define the terms i. Periodic motion ii. Oscillatory motion iii. Oscillation 13) Figure below depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)? (NCERT)
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14) Define the following terms. i. Period of oscillation
ii. Frequency
iii. Amplitude
15) Define damped oscillations? 16) Define wave. State different types of waves with suitable examples. 17) Distinguish between mechanical waves and electromagnetic waves. 18) Explain with an example particle of the medium can be set up into oscillatory motion, only if the medium possesses the property of elasticity and inertia. 19) Define progressive waves. State different types of progressive waves. 20) Define. i. Transverse progressive waves
ii. Longitudinal progressive waves.
21) Define crest and trough in a transverse wave. Show the position of crest and trough on the transverse wave graph. 22) Define compression and rarefactions. Show the position of compression and rarefaction on the longitudinal wave. 23) A solid can transmit a longitudinal or a transverse progressive wave but a fluid can transmit only the former, Why? 24) Given below are some examples of wave motion. State in each case if the wave motion is transverse, longitudinal or a combination of both: (A) Motion of a kink in a longitudinal spring produced by displacing one end of the spring sideways.
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(B) Waves produced in a cylinder containing a liquid by moving its piston back and forth. (C) Waves produced by a motorboat sailing in water. (D) Ultrasonic waves in air produced by a vibrating quartz crystal. 25) Is the frequency of a sound wave the same as the frequency of vibration of its source? 26) Define an isothermal change and adiabatic change 27) Give the Newton’s formula for the velocity of sound in air and show that the formula does not give the correct value for the speed of sound in air. 28) Show that for 1°C rise in temperature, the velocity of sound in air increases by 0.61 m/s. 29) What is musical sound? Write the characteristics of musical sound. 30) Define noise. Discuss its limitations. 31) Write short note on loudness of sound. OR Explain how loudness affects the characteristics of sound. 32) Write a short note on pitch of sound note. 33) Write short note on quality (timbre) of sound note. 34) State the factors on which loudness of sound note depends. 35) Explain the effects of following on intensity of sound. i. Amplitude
ii. Distance of source
iii. Size of the vibrating body
36) Define the following terms. i. Note
ii. Tone
iv. Overtones
v. Harmonics
iii. Fundamental tone.
37) Define consonance and dissonance. 38) Define the terms. i. Harmony
ii. Melody
iii. Musical interval.
39) Define musical scale. Explain the diatonic scale and its advantages. Also discuss its disadvantage.
❖ Textbook Problems 1) A violin string emits sound of frequency 510 Hz. How far will the sound waves reach when string completes 250 vibrations? The velocity of sound is 340 m/s. (Ans : 166.7 m) 2) The velocity of sound in air at 27oC is 340 m/s. Calculate the velocity of sound in air at 127oC.
(Ans : 392.6 m/s)
3) The velocity of sound in gas is 498 m/s and in air is 332 m/s. What is the ratio of wavelength of sound waves in gas to air?
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(Ans : 3:2) Sound Waves
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4) A human ear responds to sound waves of frequencies in the range of 20Hz to 20 KHz. What are the corresponding wavelengths, if the speed of sound in air is 330 m/s?
(Ans : 16.5 m, 0.0165 m)
5) An observer heard the thunder 5 second after the flash of lighting. What is the distance of the flash from the observer if the velocity of sound is 330 m/s? (speed of light = 3 × 108m/s)
(Ans : 1650 m)
6) A man standing between two parallel cliffs fires a gun. He hears two echoes one after 2 seconds and the other after 4 seconds. What is the distance between the cliffs if the velocity of sound is 330 m/s?
(Ans : 990 m)
7) You are at large outdoor concert, seated 300m from speaker system. The concert is also being broadcast live. Consider a listener 5000 km away who receives the broadcast. Who will hear the music first, you are listener and by what time difference? (speed of light = 3 × 108m/s and speed of sound in air = 343 m/s) (Ans : Listener, 0.8579 s) 8) The wavelength of a sound note is 1 m in air and 2.5 m in a liquid. Find the speed of sound in the liquid, if the speed of the sound in air is 330 m/s.
(Ans : 825 m/s)
9) A bat emits ultrasonic sound of frequency 1000 kHz in air. If the sound meets a water surface, what is the wavelength of (a) the reflected sound, (b) the transmitted sound? Speed in air is 340 m s-1 and in water 1486 m s-1. (Ans. (a)
(b)
)
10) Estimate the speed of sound in air at standard temperature and pressure. The mass of 1 mole of air is 29.0 × 10-3 kg.
(Ans : 279.27 m/s.)
11) The densities of nitrogen and oxygen at NTP are 1.25 kg/m3 and 1.43 kg/m3 respectively. If the speed of sound in oxygen at NTP is 320 m/s, calculate the speed in nitrogen, under the same conditions of temperature and pressure. ( the gases is 1.4)
for both
(Ans : 342.3 m/s)
12) Find the temperature at which the velocity of sound in air will be 1.5 times its velocity at 0° C.
(Ans : 341.25 °C.)
13) The wavelength of a note is 27 m in air when the temperature is 27 °C. What is the wavelength when the temperature is increased to 37 °C?
(Ans : 27.45 m)
14) At what temperature will the speed of sound in oxygen be the same as the speed of sound in carbon-dioxide at 0 °C? [Given: Molecular weights of oxygen and carbon- dioxide are 32 and 44, respectively, for carbon-dioxide and
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for oxygen.] (Ans : 192.87 K.)
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15) Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically the speed of S wave is about 4.0 km s-1, and that of P wave is 8.0 km s-1. A seismograph records P and S waves from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in straight line, at what distance does the earthquake occur?
(Ans : 1920 away)
❖ Practice Problems ➢ Type-I : Problems based on relation between
and n
1) When a tuning fork of frequency 400 Hz completed 20 vibrations, the distance covered by sound is 17.2 m. Find the wavelength and velocity of sound waves. (Ans. 0.86 m, 344 m/s) 2) A source of sound emits waves of wavelength 1.7 m in air. What is the frequency of the sound source, if the velocity of sound in air is 340 m/s?
(Ans. 200 Hz)
3) A tuning fork vibrates with a frequency of 256 Hz. If the speed of sound is find the wavelength and the distance which the sound travels during the time the fork makes 60 vibrations.
(Ans. 1.35 m, 81 m)
4) The velocity of sound in air is 336 m/s and in water it is 1440 m/s. Wavelength of sound waves in air is 1.75 m. What is the frequency and wavelength of sound waves in water?
(Ans. 192 Hz, 7.5 m)
➢ Type-II : Problems based on Newton’s and Laplace’s formula for velocity of sound 5) If the velocity of the longitudinal wave in water is 1450 m/sec, then calculate the Bulk modulus of water.
(Ans. 21 × 109 dyne/cm2)
6) If the velocity of sound in helium at N.T.P. is 1008 m/s, find the density of helium at N.T.P. (
for. helium = 1.66)
(Ans. 0.166 kg/m3)
➢ Type-III : Problems based on effect of temperature on velocity of sound 7) Find the temperature at which the velocity of sound in air is 350 m/s. [Velocity of sound in air at 0 °C is 332 m/s.]
(Ans. 30.4 °C)
8) A sounding source has a frequency of 256 Hz. If the temperature of air is 27 °C, what is the wavelength of waves sent by the source? [Velocity of sound in air at 0 °C = 331 m/s.]
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9) The wavelength of a sound note in air is 35 m at 40 °C. When the temperature is decreased to 22 °C, find its wavelength.
(Ans. 33.98 m)
10) The longitudinal waves starting from a ship, return from the bottom of the sea to the ship after 2.64 s. If the bulk modulus of water is 220 N/mm-2 and the density calculate the depth of the sea. [g = 9.8 N kg-1] 11)
(Ans. 1848 m)
A wave disturbance has a wavelength of 0.05 m. Find the number of waves in a distance of one metre.
(Ans. 20 m-1)
12) Two sounding sources with their frequencies of vibration differing by 6 Hz per second, send waves in air of wavelengths 50 cm and 50.5 cm respectively. Find the velocity of sound in air.
(Ans. 303 m/s)
❖ Multiple Choice Question 1) When a sound wave moves from one medium to another, the quantity that remains unchanged is _________. (A) frequency
(B) amplitude
(C) wavelength
(D) speed
2) Water waves are_________. (A) longitudinal
(C) both longitudinal and transverse
(B) transverse
(D) neither longitudinal nor transverse
3) Sound travels fastest in__________. (A) water
(B) air
(C) steel
(D) kerosene oil
4) At room temperature, velocity of sound in air at 10 atmospheric pressure and at 1 atmospheric pressure will be in the ratio (A) 10 : 1
(B)1 : 10
(C) 1 : 1
(D) cannot say
5) In a gas, velocity of sound varies directly as (A) square root of isothermal elasticity. (B) square of isothermal elasticity. (C) square root of adiabatic elasticity. (D) adiabatic elasticity. 6) Laplace’s correction was needed in Newton’s formula of velocity of sound because sound waves in air __________. (A) are longitudinal
(C) propagate isothermally
(B) are transverse
(D) propagate adiabatically
7) At a given temperature, velocity of sound in oxygen and in hydrogen has the ratio (A) 4 : 1
(B) 1 : 4
(C) 1 : 1
(D) 2 : 1
8) With decrease in water vapour content in air, velocity of sound ________. (A) increases
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(C) remains constant Sound Waves
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9) The temperature at which speed of sound in air becomes double its value at 0 °C is (A) 546 °C
(B) 819 °C
(C) 273 °C
(D) 1092 °C
10) Human ear cannot hear those mechanical waves whose frequency lies in the frequency range (A) less than 100Hz but greater than 10000 Hz (B) between 1000 Hz and 500 Hz (C) between 500 Hz and 20000 Hz (D) less than 16 Hz and more than 20000 Hz. 11) The velocity of sound in air at NTP is 330 m/s. What will be its value when temperature is doubled and pressure is halved ? (A) 330 m/s
(C) 330
(B) 165 m/s
(D)
m/s
m/s
12) A series of ocean waves, each 5.0 m from crest to crest, moving past the observer at a rate of 2 waves per second have wave velocity (A) 2.5 m/s
(B) 5.0 m/s
(C) 8.0 m/s
(D) 10.0 m/s
13) A radio station broadcasts at 760 kHz. What is the wavelength of the station ? (A) 395 m
(B) 790 m
(C) 760 m
(D) 197.5 m
14) If the bulk modulus of water is 2100 MPa, what is the speed of sound in water ? (A) 1450 m/s
(B) 2100 m/s
(C) 0.21 m/s
(D) 21 m/s
15) If speed of sound in air at 0°C is 331 m/s. What will be its value at 35° C? (A) 331 m/s
(B) 366 m/s
(C) 351.6 m/s
(D) 332 m/s.
16) For a progressive wave, in the usual notation (A)
(B)
(C)
(D)
17) The density of moist air is less than that of (A) air
(B) dry air
(C) cold air
(D) impure air
18) Speed of sound in any gas (A) does not depend upon density of the gas. (B) does not depend upon changes in pressure.
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(C) does not depend upon temperature. (D) depends upon density of the gas. 19) If pressure of air gets doubled then velocity of sound in air ________. (A) gets doubled
(C)
times initial velocity
(B) remains unchanged
(D) becomes half
20) Wave motion has (A) single periodicity.
(C) only periodicity in space.
(B) double periodicity.
(D) only periodicity in time.
21) Oscillations of a particle are opposed by (A) resistive forces due to medium.
(C) electrostatic force between them.
(B) gravitational force between them. (D) force due to velocity. 22) Select the correct statement. (A) In a wave, not the energy but matter is transferred from one point to another point. (B) In a wave, neither the energy nor the matter is transferred from one point to another point. (C) In a wave, only the energy and not the matter is transferred from one point to another point. (D) In a wave, both the energy and matter is transferred from one point to another point. 23) Dimensions of wavelength of progressive wave is (A) [L0M0T1]
(B) [L-1M0T0]
(C) [L0M1T0]
(D) [L1M0T0]
24) The speed of the wave is controlled by (A) elasticity of the medium only.
(C) elasticity and inertia of medium.
(B) inertia of medium only.
(D) initial speed.
25) Longitudinal waves CANNOT be ________. (A) reflected
(B) refracted
(C) scattered
(D) polarised
26) Wavelength of the transverse wave is 30 cm. If the particle at some instant has displacement 2 cm, find the displacement of the particle 15 cm away at the same instant. (A) 2 cm
(B) 17 cm
(C) -2 cm
(D) -17 cm
27) The wavelength of sound in air is 1.5 m and that in liquid is 2 m. If the velocity of sound in air is 330 m/s, the velocity of sound in liquid is (A) 330 m/s
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(B) 440 m/s
(C) 495 m/s
(D) 660 m/s
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28) The velocity of sound in a gas is 340 m/s at the pressure P, what will be the velocity of the gas when only pressure is doubled and temperature same? (A) 170 m/s
(B) 243 m/s
(C) 340 m/s
(D) 680 m/s
29) A music interval 8:5 is ________. (A) sharp
(C) imperfectly consonant
(B) discordant
(D) perfectly consonant
30) Choose the correct statement. (A) For 1 째C rise in temperature, velocity of sound increases by 0.61 m/s. (B) For 1 째C rise in temperature, velocity of sound decreases by 0.61 m/s. (C) For 1 째C rise in temperature, velocity of sound decreases by
m/s.
(D) For 1 째C rise in temperature, velocity of sound increases by
m/s
31) For a transverse wave, the distance between two successive crests is 2 m. If 4 troughs cross a given point along the direction of travel in 20 s, the distance between a crest and trough is (A) 0.2 m
(B) 1 m
(C) 8m
(D) 10 m
32) A sound note emitted from a certain source has a velocity of 300 m/s in air and 1050 m/s in water. If the wavelength of sound note in air is 2 m, the wavelength in water is (A) 2 m
(B) 6 m
(C) 7 m
33) Wavelengths of two sound waves in air are
(D) 12 m m and
m, the difference between
their frequencies is 9, the velocity of sound in air is (A) 300 m/s
(B) 310 m/s
(C) 330 m/s
(D) 373.5 m/s
34) A tuning fork has frequency 512 Hz. Find the number of vibrations of the fork in the time for which the sound from the tuning fork reaches 332 m in air. (velocity of sound in air is 332 m/s.) (A) 100
(B) 200
(C) 332
(D) 512
35) Two tuning forks have frequencies 320 Hz and 340 Hz. They emit sound notes differing in wavelength by 6 cm in air, the velocity of sound in air is (A) 340 m/s
(B) 326.4 m/s
(C) 320 m/s
(D) 300 m/s
36) The wavelength of radiowave of frequency 500 MHz is (velocity of radio wave (A) 0.3 m
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(B) 0.5 m
m/s) (C) 0.6 m
(D) 1.5 m
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37) A thunder clap was heard 6 seconds after a lightening flash was seen. If the speed of sound in air is 340 m/s at the time of observation, the distance of the listener from the thunder clap is (A) 56.6 m
(B) 346 m
(C) 1020 m
(D) 2040 m
38) The speed of sound in air at NTP is 330 m/s. The period of sound wave of wavelength 66 cm is (A) 0.2 s
(B) 0.1 s
(C) 0.1 × 10-2 s
(D) 0.2 × 10-2 s
39) If the velocity of sound in hydrogen is 1248 m/s, the velocity of sound in oxygen is [Given: (A) 1248 m/s
] (B) 624 m/s
(C) 312 m/s
(D) 300 m/s
➢ Answers To Multiple Choice Questions 1. (A)
2. (C)
3. (C)
4. (C)
5. (C)
6. (D)
7. (B)
8. (B)
9. (B)
10. (D)
11. (D)
12. (C)
13. (A)
14. (A)
15. (C)
16. (B)
17. (B)
18. (D)
19. (C)
20. (B)
21. (A)
22. (C)
23. (D)
24. (C)
25. (D)
26. (C)
27. (B)
28. (C)
29. (C)
30. (A)
31. (B)
32. (C)
33. (D)
34. (C)
35. (B)
36. (C)
37. (D)
38. (D)
39. (C)
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